%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG143+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n032.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 18:30:20 EDT 2022 % Result : Unsatisfiable 8.45s 8.70s % Output : Proof 8.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : ALG143+1 : TPTP v8.1.0. Released v2.7.0. % 0.08/0.10 % Command : run_zenon %s %d % 0.10/0.29 % Computer : n032.cluster.edu % 0.10/0.29 % Model : x86_64 x86_64 % 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.29 % Memory : 8042.1875MB % 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.29 % CPULimit : 300 % 0.10/0.29 % WCLimit : 600 % 0.10/0.29 % DateTime : Tue Jun 7 22:25:51 EDT 2022 % 0.10/0.29 % CPUTime : % 8.45/8.70 (* PROOF-FOUND *) % 8.45/8.70 % SZS status Unsatisfiable % 8.45/8.70 (* BEGIN-PROOF *) % 8.45/8.70 % SZS output start Proof % 8.45/8.70 Theorem zenon_thm : False. % 8.45/8.70 Proof. % 8.45/8.70 assert (zenon_L1_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H1d zenon_H1e zenon_H1f. % 8.45/8.70 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H20 | zenon_intro zenon_H21 ]. % 8.45/8.70 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (e0)) = (op (e0) (e1)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H1f. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H20. % 8.45/8.70 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 8.45/8.70 cut (((op (e0) (e1)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e0) (e0)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H22. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H1d. % 8.45/8.70 cut (((e0) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 8.45/8.70 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H21. apply refl_equal. % 8.45/8.70 apply zenon_H23. apply sym_equal. exact zenon_H1e. % 8.45/8.70 apply zenon_H21. apply refl_equal. % 8.45/8.70 apply zenon_H21. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L1_ *) % 8.45/8.70 assert (zenon_L2_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H24 zenon_H1e zenon_H25. % 8.45/8.70 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H26 | zenon_intro zenon_H27 ]. % 8.45/8.70 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e0)) = (op (e0) (e2)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H25. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H26. % 8.45/8.70 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 8.45/8.70 cut (((op (e0) (e2)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H28]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e0) (e0)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H28. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H24. % 8.45/8.70 cut (((e0) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 8.45/8.70 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H27. apply refl_equal. % 8.45/8.70 apply zenon_H23. apply sym_equal. exact zenon_H1e. % 8.45/8.70 apply zenon_H27. apply refl_equal. % 8.45/8.70 apply zenon_H27. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L2_ *) % 8.45/8.70 assert (zenon_L3_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H29 zenon_H2a zenon_H2b. % 8.45/8.70 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H2c | zenon_intro zenon_H2d ]. % 8.45/8.70 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e1)) = (op (e1) (e2)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H2b. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H2c. % 8.45/8.70 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 8.45/8.70 cut (((op (e1) (e2)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e1) (e1)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H2e. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H29. % 8.45/8.70 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 8.45/8.70 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H2d. apply refl_equal. % 8.45/8.70 apply zenon_H2f. apply sym_equal. exact zenon_H2a. % 8.45/8.70 apply zenon_H2d. apply refl_equal. % 8.45/8.70 apply zenon_H2d. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L3_ *) % 8.45/8.70 assert (zenon_L4_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H30 zenon_H1e zenon_H31. % 8.45/8.70 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H32 | zenon_intro zenon_H33 ]. % 8.45/8.70 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e0)) = (op (e0) (e3)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H31. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H32. % 8.45/8.70 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 8.45/8.70 cut (((op (e0) (e3)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e0) (e0)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H34. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H30. % 8.45/8.70 cut (((e0) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 8.45/8.70 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H33. apply refl_equal. % 8.45/8.70 apply zenon_H23. apply sym_equal. exact zenon_H1e. % 8.45/8.70 apply zenon_H33. apply refl_equal. % 8.45/8.70 apply zenon_H33. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L4_ *) % 8.45/8.70 assert (zenon_L5_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H35 zenon_H2a zenon_H36. % 8.45/8.70 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H37 | zenon_intro zenon_H38 ]. % 8.45/8.70 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e1)) = (op (e1) (e3)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H36. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H37. % 8.45/8.70 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 8.45/8.70 cut (((op (e1) (e3)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e1) (e1)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H39. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H35. % 8.45/8.70 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 8.45/8.70 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H38. apply refl_equal. % 8.45/8.70 apply zenon_H2f. apply sym_equal. exact zenon_H2a. % 8.45/8.70 apply zenon_H38. apply refl_equal. % 8.45/8.70 apply zenon_H38. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L5_ *) % 8.45/8.70 assert (zenon_L6_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 8.45/8.70 do 0 intro. intros zenon_H3a zenon_H3b zenon_H3c. % 8.45/8.70 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e2) (e3)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H3a. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H3b. % 8.45/8.70 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H3d]. % 8.45/8.70 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H3e. apply refl_equal. % 8.45/8.70 apply zenon_H3d. apply sym_equal. exact zenon_H3c. % 8.45/8.70 (* end of lemma zenon_L6_ *) % 8.45/8.70 assert (zenon_L7_ : (~((e0) = (e0))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H3f. % 8.45/8.70 apply zenon_H3f. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L7_ *) % 8.45/8.70 assert (zenon_L8_ : (~((e1) = (e1))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H40. % 8.45/8.70 apply zenon_H40. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L8_ *) % 8.45/8.70 assert (zenon_L9_ : (~((op (e1) (op (e1) (e1))) = (e1))) -> ((op (e1) (e1)) = (e1)) -> False). % 8.45/8.70 do 0 intro. intros zenon_H41 zenon_H2a. % 8.45/8.70 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (op (e1) (e1))) = (e1))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H41. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H2a. % 8.45/8.70 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.70 cut (((op (e1) (e1)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H42]. % 8.45/8.70 congruence. % 8.45/8.70 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_H43 | zenon_intro zenon_H44 ]. % 8.45/8.70 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e1)) = (op (e1) (op (e1) (e1))))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H42. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H43. % 8.45/8.70 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 8.45/8.70 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e1) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 8.45/8.70 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H40. apply refl_equal. % 8.45/8.70 exact (zenon_H46 zenon_H2a). % 8.45/8.70 apply zenon_H44. apply refl_equal. % 8.45/8.70 apply zenon_H44. apply refl_equal. % 8.45/8.70 apply zenon_H40. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L9_ *) % 8.45/8.70 assert (zenon_L10_ : ((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3)))))) -> ((op (e1) (e1)) = (e1)) -> False). % 8.45/8.70 do 0 intro. intros zenon_H47 zenon_H2a. % 8.45/8.70 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 8.45/8.70 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H41. zenon_intro zenon_H4a. % 8.45/8.70 apply (zenon_L9_); trivial. % 8.45/8.70 (* end of lemma zenon_L10_ *) % 8.45/8.70 assert (zenon_L11_ : (~((e2) = (e2))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H4b. % 8.45/8.70 apply zenon_H4b. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L11_ *) % 8.45/8.70 assert (zenon_L12_ : (~((op (e2) (op (e2) (e2))) = (e2))) -> ((op (e2) (e2)) = (e2)) -> False). % 8.45/8.70 do 0 intro. intros zenon_H4c zenon_H3b. % 8.45/8.70 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (op (e2) (e2))) = (e2))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H4c. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H3b. % 8.45/8.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.70 cut (((op (e2) (e2)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 8.45/8.70 congruence. % 8.45/8.70 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H4e | zenon_intro zenon_H4f ]. % 8.45/8.70 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((op (e2) (e2)) = (op (e2) (op (e2) (e2))))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H4d. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H4e. % 8.45/8.70 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 8.45/8.70 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e2) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H51]. % 8.45/8.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H4b. apply refl_equal. % 8.45/8.70 exact (zenon_H51 zenon_H3b). % 8.45/8.70 apply zenon_H4f. apply refl_equal. % 8.45/8.70 apply zenon_H4f. apply refl_equal. % 8.45/8.70 apply zenon_H4b. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L12_ *) % 8.45/8.70 assert (zenon_L13_ : ((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3)))))) -> ((op (e2) (e2)) = (e2)) -> False). % 8.45/8.70 do 0 intro. intros zenon_H52 zenon_H3b. % 8.45/8.70 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 8.45/8.70 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 8.45/8.70 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H4c. zenon_intro zenon_H57. % 8.45/8.70 apply (zenon_L12_); trivial. % 8.45/8.70 (* end of lemma zenon_L13_ *) % 8.45/8.70 assert (zenon_L14_ : (~((e3) = (e3))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H58. % 8.45/8.70 apply zenon_H58. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L14_ *) % 8.45/8.70 assert (zenon_L15_ : (~((op (e3) (op (e3) (e3))) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 8.45/8.70 do 0 intro. intros zenon_H59 zenon_H5a. % 8.45/8.70 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (op (e3) (e3))) = (e3))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H59. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H5a. % 8.45/8.70 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.45/8.70 cut (((op (e3) (e3)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 8.45/8.70 congruence. % 8.45/8.70 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 8.45/8.70 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((op (e3) (e3)) = (op (e3) (op (e3) (e3))))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H5b. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H5c. % 8.45/8.70 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 8.45/8.70 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e3) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 8.45/8.70 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H58. apply refl_equal. % 8.45/8.70 exact (zenon_H5f zenon_H5a). % 8.45/8.70 apply zenon_H5d. apply refl_equal. % 8.45/8.70 apply zenon_H5d. apply refl_equal. % 8.45/8.70 apply zenon_H58. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L15_ *) % 8.45/8.70 assert (zenon_L16_ : ((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3)))))) -> ((op (e3) (e3)) = (e3)) -> False). % 8.45/8.70 do 0 intro. intros zenon_H60 zenon_H5a. % 8.45/8.70 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 8.45/8.70 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 8.45/8.70 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H59. % 8.45/8.70 apply (zenon_L15_); trivial. % 8.45/8.70 (* end of lemma zenon_L16_ *) % 8.45/8.70 assert (zenon_L17_ : ((op (e0) (e0)) = (e0)) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H1e zenon_H66 zenon_H67. % 8.45/8.70 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H68 | zenon_intro zenon_H40 ]. % 8.45/8.70 cut (((e1) = (e1)) = ((e0) = (e1))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H67. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H68. % 8.45/8.70 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.70 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e0) (e0)) = (e0)) = ((e1) = (e0))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H69. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H1e. % 8.45/8.70 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.45/8.70 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 8.45/8.70 congruence. % 8.45/8.70 exact (zenon_H6a zenon_H66). % 8.45/8.70 apply zenon_H3f. apply refl_equal. % 8.45/8.70 apply zenon_H40. apply refl_equal. % 8.45/8.70 apply zenon_H40. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L17_ *) % 8.45/8.70 assert (zenon_L18_ : ((op (e1) (e1)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H2a zenon_H6b zenon_H6c. % 8.45/8.70 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H6d | zenon_intro zenon_H6e ]. % 8.45/8.70 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e0) (e1)) = (op (e1) (e1)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H6c. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H6d. % 8.45/8.70 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 8.45/8.70 cut (((op (e1) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e0) (e1)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H6f. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H2a. % 8.45/8.70 cut (((e1) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 8.45/8.70 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H6e. apply refl_equal. % 8.45/8.70 apply zenon_H70. apply sym_equal. exact zenon_H6b. % 8.45/8.70 apply zenon_H6e. apply refl_equal. % 8.45/8.70 apply zenon_H6e. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L18_ *) % 8.45/8.70 assert (zenon_L19_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H71 zenon_H66 zenon_H25. % 8.45/8.70 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H26 | zenon_intro zenon_H27 ]. % 8.45/8.70 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e0)) = (op (e0) (e2)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H25. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H26. % 8.45/8.70 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 8.45/8.70 cut (((op (e0) (e2)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H28]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e0) (e0)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H28. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H71. % 8.45/8.70 cut (((e1) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 8.45/8.70 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H27. apply refl_equal. % 8.45/8.70 apply zenon_H72. apply sym_equal. exact zenon_H66. % 8.45/8.70 apply zenon_H27. apply refl_equal. % 8.45/8.70 apply zenon_H27. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L19_ *) % 8.45/8.70 assert (zenon_L20_ : ((op (e1) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H2a zenon_H73 zenon_H74. % 8.45/8.70 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H6d | zenon_intro zenon_H6e ]. % 8.45/8.70 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (e0)) = (op (e1) (e1)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H74. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H6d. % 8.45/8.70 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 8.45/8.70 cut (((op (e1) (e1)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e1) (e0)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H75. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H2a. % 8.45/8.70 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 8.45/8.70 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H6e. apply refl_equal. % 8.45/8.70 apply zenon_H76. apply sym_equal. exact zenon_H73. % 8.45/8.70 apply zenon_H6e. apply refl_equal. % 8.45/8.70 apply zenon_H6e. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L20_ *) % 8.45/8.70 assert (zenon_L21_ : ((op (e0) (e0)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H1e zenon_H77 zenon_H78. % 8.45/8.70 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H79 | zenon_intro zenon_H4b ]. % 8.45/8.70 cut (((e2) = (e2)) = ((e0) = (e2))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H78. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H79. % 8.45/8.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.70 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e0) (e0)) = (e0)) = ((e2) = (e0))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H7a. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H1e. % 8.45/8.70 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.45/8.70 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 8.45/8.70 congruence. % 8.45/8.70 exact (zenon_H7b zenon_H77). % 8.45/8.70 apply zenon_H3f. apply refl_equal. % 8.45/8.70 apply zenon_H4b. apply refl_equal. % 8.45/8.70 apply zenon_H4b. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L21_ *) % 8.45/8.70 assert (zenon_L22_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e1))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H24 zenon_H71 zenon_H67. % 8.45/8.70 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H68 | zenon_intro zenon_H40 ]. % 8.45/8.70 cut (((e1) = (e1)) = ((e0) = (e1))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H67. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H68. % 8.45/8.70 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.70 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e0) (e2)) = (e0)) = ((e1) = (e0))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H69. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H24. % 8.45/8.70 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.45/8.70 cut (((op (e0) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 8.45/8.70 congruence. % 8.45/8.70 exact (zenon_H7c zenon_H71). % 8.45/8.70 apply zenon_H3f. apply refl_equal. % 8.45/8.70 apply zenon_H40. apply refl_equal. % 8.45/8.70 apply zenon_H40. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L22_ *) % 8.45/8.70 assert (zenon_L23_ : (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> False). % 8.45/8.70 do 0 intro. intros zenon_H7d zenon_H7e zenon_H71. % 8.45/8.70 cut (((op (e0) (e2)) = (e2)) = ((e1) = (e2))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H7d. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H7e. % 8.45/8.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.70 cut (((op (e0) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 8.45/8.70 congruence. % 8.45/8.70 exact (zenon_H7c zenon_H71). % 8.45/8.70 apply zenon_H4b. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L23_ *) % 8.45/8.70 assert (zenon_L24_ : (~((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))) -> ((op (e2) (e2)) = (e0)) -> False). % 8.45/8.70 do 0 intro. intros zenon_H7f zenon_H80. % 8.45/8.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.70 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 8.45/8.70 congruence. % 8.45/8.70 exact (zenon_H81 zenon_H80). % 8.45/8.70 apply zenon_H4b. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L24_ *) % 8.45/8.70 assert (zenon_L25_ : ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (op (op (e2) (e2)) (e2)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H71 zenon_H80 zenon_H82. % 8.45/8.70 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H83 | zenon_intro zenon_H84 ]. % 8.45/8.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e1) = (op (op (e2) (e2)) (e2)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H82. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H83. % 8.45/8.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 8.45/8.70 cut (((op (op (e2) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e0) (e2)) = (e1)) = ((op (op (e2) (e2)) (e2)) = (e1))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H85. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H71. % 8.45/8.70 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.70 cut (((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 8.45/8.70 congruence. % 8.45/8.70 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H83 | zenon_intro zenon_H84 ]. % 8.45/8.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H86. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H83. % 8.45/8.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 8.45/8.70 cut (((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 8.45/8.70 congruence. % 8.45/8.70 apply (zenon_L24_); trivial. % 8.45/8.70 apply zenon_H84. apply refl_equal. % 8.45/8.70 apply zenon_H84. apply refl_equal. % 8.45/8.70 apply zenon_H40. apply refl_equal. % 8.45/8.70 apply zenon_H84. apply refl_equal. % 8.45/8.70 apply zenon_H84. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L25_ *) % 8.45/8.70 assert (zenon_L26_ : ((op (e1) (e0)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> False). % 8.45/8.70 do 0 intro. intros zenon_H87 zenon_H71 zenon_H80. % 8.45/8.70 apply (zenon_notand_s _ _ ax9); [ zenon_intro zenon_H89 | zenon_intro zenon_H88 ]. % 8.45/8.70 apply zenon_H89. apply sym_equal. exact zenon_H80. % 8.45/8.70 apply (zenon_notand_s _ _ zenon_H88); [ zenon_intro zenon_H8a | zenon_intro zenon_H82 ]. % 8.45/8.70 elim (classic ((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ]. % 8.45/8.70 cut (((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2)))) = ((e3) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H8a. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H8b. % 8.45/8.70 cut (((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 8.45/8.70 cut (((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H8d]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e1) (e0)) = (e3)) = ((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (e3))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H8d. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H87. % 8.45/8.70 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.45/8.70 cut (((op (e1) (e0)) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 8.45/8.70 congruence. % 8.45/8.70 elim (classic ((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ]. % 8.45/8.70 cut (((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2)))) = ((op (e1) (e0)) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H8e. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H8b. % 8.45/8.70 cut (((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 8.45/8.70 cut (((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 8.45/8.70 cut (((op (op (e2) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e0) (e2)) = (e1)) = ((op (op (e2) (e2)) (e2)) = (e1))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H85. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H71. % 8.45/8.70 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.70 cut (((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 8.45/8.70 congruence. % 8.45/8.70 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H83 | zenon_intro zenon_H84 ]. % 8.45/8.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H86. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H83. % 8.45/8.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 8.45/8.70 cut (((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 8.45/8.70 congruence. % 8.45/8.70 apply (zenon_L24_); trivial. % 8.45/8.70 apply zenon_H84. apply refl_equal. % 8.45/8.70 apply zenon_H84. apply refl_equal. % 8.45/8.70 apply zenon_H40. apply refl_equal. % 8.45/8.70 exact (zenon_H81 zenon_H80). % 8.45/8.70 apply zenon_H8c. apply refl_equal. % 8.45/8.70 apply zenon_H8c. apply refl_equal. % 8.45/8.70 apply zenon_H58. apply refl_equal. % 8.45/8.70 apply zenon_H8c. apply refl_equal. % 8.45/8.70 apply zenon_H8c. apply refl_equal. % 8.45/8.70 apply (zenon_L25_); trivial. % 8.45/8.70 (* end of lemma zenon_L26_ *) % 8.45/8.70 assert (zenon_L27_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 8.45/8.70 do 0 intro. intros zenon_H90 zenon_H71 zenon_H91. % 8.45/8.70 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e2) (e2)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H90. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H71. % 8.45/8.70 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H92]. % 8.45/8.70 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H27. apply refl_equal. % 8.45/8.70 apply zenon_H92. apply sym_equal. exact zenon_H91. % 8.45/8.70 (* end of lemma zenon_L27_ *) % 8.45/8.70 assert (zenon_L28_ : ((op (e2) (e2)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H3b zenon_H93 zenon_H94. % 8.45/8.70 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H3e ]. % 8.45/8.70 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e1) (e2)) = (op (e2) (e2)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H94. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H95. % 8.45/8.70 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 8.45/8.70 cut (((op (e2) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e1) (e2)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H96. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H3b. % 8.45/8.70 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 8.45/8.70 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H3e. apply refl_equal. % 8.45/8.70 apply zenon_H97. apply sym_equal. exact zenon_H93. % 8.45/8.70 apply zenon_H3e. apply refl_equal. % 8.45/8.70 apply zenon_H3e. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L28_ *) % 8.45/8.70 assert (zenon_L29_ : ((op (e3) (e2)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H98 zenon_H99 zenon_H9a. % 8.45/8.70 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H9b | zenon_intro zenon_H9c ]. % 8.45/8.70 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e2) (e2)) = (op (e3) (e2)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H9a. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H9b. % 8.45/8.70 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 8.45/8.70 cut (((op (e3) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e2) (e2)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H9d. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H98. % 8.45/8.70 cut (((e3) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 8.45/8.70 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H9c. apply refl_equal. % 8.45/8.70 apply zenon_H9e. apply sym_equal. exact zenon_H99. % 8.45/8.70 apply zenon_H9c. apply refl_equal. % 8.45/8.70 apply zenon_H9c. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L29_ *) % 8.45/8.70 assert (zenon_L30_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H9f zenon_H87 zenon_H71 zenon_H90 zenon_H94 zenon_H93 zenon_H98 zenon_H9a. % 8.45/8.70 apply (zenon_or_s _ _ zenon_H9f); [ zenon_intro zenon_H80 | zenon_intro zenon_Ha0 ]. % 8.45/8.70 apply (zenon_L26_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Ha0); [ zenon_intro zenon_H91 | zenon_intro zenon_Ha1 ]. % 8.45/8.70 apply (zenon_L27_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Ha1); [ zenon_intro zenon_H3b | zenon_intro zenon_H99 ]. % 8.45/8.70 apply (zenon_L28_); trivial. % 8.45/8.70 apply (zenon_L29_); trivial. % 8.45/8.70 (* end of lemma zenon_L30_ *) % 8.45/8.70 assert (zenon_L31_ : ((op (e1) (e1)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H2a zenon_Ha2 zenon_Ha3. % 8.45/8.70 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H58 ]. % 8.45/8.70 cut (((e3) = (e3)) = ((e1) = (e3))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Ha3. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_Ha4. % 8.45/8.70 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.45/8.70 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e1) (e1)) = (e1)) = ((e3) = (e1))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Ha5. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H2a. % 8.45/8.70 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.70 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 8.45/8.70 congruence. % 8.45/8.70 exact (zenon_Ha6 zenon_Ha2). % 8.45/8.70 apply zenon_H40. apply refl_equal. % 8.45/8.70 apply zenon_H58. apply refl_equal. % 8.45/8.70 apply zenon_H58. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L31_ *) % 8.45/8.70 assert (zenon_L32_ : ((op (e1) (e2)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H93 zenon_Ha7 zenon_Ha8. % 8.45/8.70 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H58 ]. % 8.45/8.70 cut (((e3) = (e3)) = ((e2) = (e3))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Ha8. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_Ha4. % 8.45/8.70 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.45/8.70 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e1) (e2)) = (e2)) = ((e3) = (e2))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Ha9. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H93. % 8.45/8.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.70 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 8.45/8.70 congruence. % 8.45/8.70 exact (zenon_Haa zenon_Ha7). % 8.45/8.70 apply zenon_H4b. apply refl_equal. % 8.45/8.70 apply zenon_H58. apply refl_equal. % 8.45/8.70 apply zenon_H58. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L32_ *) % 8.45/8.70 assert (zenon_L33_ : (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> False). % 8.45/8.70 do 0 intro. intros zenon_Hab zenon_Hac zenon_Had. % 8.45/8.70 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (e0)) = (op (e1) (e2)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Hab. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_Hac. % 8.45/8.70 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 8.45/8.70 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_Haf. apply refl_equal. % 8.45/8.70 apply zenon_Hae. apply sym_equal. exact zenon_Had. % 8.45/8.70 (* end of lemma zenon_L33_ *) % 8.45/8.70 assert (zenon_L34_ : ((op (e1) (e2)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H93 zenon_Hb0 zenon_Hab. % 8.45/8.70 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H2c | zenon_intro zenon_H2d ]. % 8.45/8.70 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e0)) = (op (e1) (e2)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Hab. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H2c. % 8.45/8.70 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 8.45/8.70 cut (((op (e1) (e2)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (e2)) = (op (e1) (e0)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Hb1. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H93. % 8.45/8.70 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 8.45/8.70 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H2d. apply refl_equal. % 8.45/8.70 apply zenon_Hb2. apply sym_equal. exact zenon_Hb0. % 8.45/8.70 apply zenon_H2d. apply refl_equal. % 8.45/8.70 apply zenon_H2d. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L34_ *) % 8.45/8.70 assert (zenon_L35_ : ((op (e1) (e3)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_Hb3 zenon_H87 zenon_Hb4. % 8.45/8.70 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H37 | zenon_intro zenon_H38 ]. % 8.45/8.70 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e0)) = (op (e1) (e3)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Hb4. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H37. % 8.45/8.70 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 8.45/8.70 cut (((op (e1) (e3)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e1) (e3)) = (e3)) = ((op (e1) (e3)) = (op (e1) (e0)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Hb5. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_Hb3. % 8.45/8.70 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 8.45/8.70 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H38. apply refl_equal. % 8.45/8.70 apply zenon_Hb6. apply sym_equal. exact zenon_H87. % 8.45/8.70 apply zenon_H38. apply refl_equal. % 8.45/8.70 apply zenon_H38. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L35_ *) % 8.45/8.70 assert (zenon_L36_ : (((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) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_Hb7 zenon_Had zenon_H74 zenon_H2a zenon_Hab zenon_H93 zenon_Hb3 zenon_Hb4. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hac | zenon_intro zenon_Hb8 ]. % 8.45/8.70 apply (zenon_L33_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb9 ]. % 8.45/8.70 apply (zenon_L20_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H87 ]. % 8.45/8.70 apply (zenon_L34_); trivial. % 8.45/8.70 apply (zenon_L35_); trivial. % 8.45/8.70 (* end of lemma zenon_L36_ *) % 8.45/8.70 assert (zenon_L37_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((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) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_Hba zenon_H9a zenon_H98 zenon_H94 zenon_H90 zenon_H71 zenon_H9f zenon_Ha3 zenon_Ha8 zenon_Hb7 zenon_Had zenon_H74 zenon_H2a zenon_Hab zenon_H93 zenon_Hb4. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.45/8.70 apply (zenon_L30_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.45/8.70 apply (zenon_L31_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.45/8.70 apply (zenon_L32_); trivial. % 8.45/8.70 apply (zenon_L36_); trivial. % 8.45/8.70 (* end of lemma zenon_L37_ *) % 8.45/8.70 assert (zenon_L38_ : (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e2)) -> False). % 8.45/8.70 do 0 intro. intros zenon_Ha8 zenon_H98 zenon_Hbd. % 8.45/8.70 cut (((op (e3) (e2)) = (e3)) = ((e2) = (e3))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Ha8. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H98. % 8.45/8.70 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.45/8.70 cut (((op (e3) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 8.45/8.70 congruence. % 8.45/8.70 exact (zenon_Hbe zenon_Hbd). % 8.45/8.70 apply zenon_H58. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L38_ *) % 8.45/8.70 assert (zenon_L39_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.45/8.70 do 0 intro. intros zenon_Hbf zenon_H7d zenon_Hb4 zenon_Hab zenon_H2a zenon_H74 zenon_Had zenon_Hb7 zenon_Ha3 zenon_H9f zenon_H71 zenon_H90 zenon_H94 zenon_H9a zenon_Hba zenon_H3c zenon_H3a zenon_Ha8 zenon_H98. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H7e | zenon_intro zenon_Hc0 ]. % 8.45/8.70 apply (zenon_L23_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H93 | zenon_intro zenon_Hc1 ]. % 8.45/8.70 apply (zenon_L37_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H3b | zenon_intro zenon_Hbd ]. % 8.45/8.70 apply (zenon_L6_); trivial. % 8.45/8.70 apply (zenon_L38_); trivial. % 8.45/8.70 (* end of lemma zenon_L39_ *) % 8.45/8.70 assert (zenon_L40_ : (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> False). % 8.45/8.70 do 0 intro. intros zenon_H78 zenon_H3b zenon_H80. % 8.45/8.70 cut (((op (e2) (e2)) = (e2)) = ((e0) = (e2))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H78. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H3b. % 8.45/8.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.70 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 8.45/8.70 congruence. % 8.45/8.70 exact (zenon_H81 zenon_H80). % 8.45/8.70 apply zenon_H4b. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L40_ *) % 8.45/8.70 assert (zenon_L41_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.45/8.70 do 0 intro. intros zenon_Hbf zenon_H71 zenon_H7d zenon_Hab zenon_Hb0 zenon_H80 zenon_H78 zenon_Ha8 zenon_H98. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H7e | zenon_intro zenon_Hc0 ]. % 8.45/8.70 apply (zenon_L23_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H93 | zenon_intro zenon_Hc1 ]. % 8.45/8.70 apply (zenon_L34_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H3b | zenon_intro zenon_Hbd ]. % 8.45/8.70 apply (zenon_L40_); trivial. % 8.45/8.70 apply (zenon_L38_); trivial. % 8.45/8.70 (* end of lemma zenon_L41_ *) % 8.45/8.70 assert (zenon_L42_ : (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> False). % 8.45/8.70 do 0 intro. intros zenon_Hc2 zenon_H98 zenon_Hc3. % 8.45/8.70 cut (((op (e3) (e2)) = (e3)) = ((e0) = (e3))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Hc2. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H98. % 8.45/8.70 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.45/8.70 cut (((op (e3) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hc4]. % 8.45/8.70 congruence. % 8.45/8.70 exact (zenon_Hc4 zenon_Hc3). % 8.45/8.70 apply zenon_H58. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L42_ *) % 8.45/8.70 assert (zenon_L43_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.45/8.70 do 0 intro. intros zenon_Hc5 zenon_H67 zenon_H3a zenon_H3c zenon_Hba zenon_H9a zenon_H94 zenon_H90 zenon_H9f zenon_Ha3 zenon_Hb7 zenon_H74 zenon_H2a zenon_Hb4 zenon_Ha8 zenon_H78 zenon_Hb0 zenon_Hab zenon_H7d zenon_H71 zenon_Hbf zenon_Hc2 zenon_H98. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_H24 | zenon_intro zenon_Hc6 ]. % 8.45/8.70 apply (zenon_L22_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Had | zenon_intro zenon_Hc7 ]. % 8.45/8.70 apply (zenon_L39_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H80 | zenon_intro zenon_Hc3 ]. % 8.45/8.70 apply (zenon_L41_); trivial. % 8.45/8.70 apply (zenon_L42_); trivial. % 8.45/8.70 (* end of lemma zenon_L43_ *) % 8.45/8.70 assert (zenon_L44_ : (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> False). % 8.45/8.70 do 0 intro. intros zenon_H7d zenon_Hc8 zenon_Hc9. % 8.45/8.70 cut (((op (e2) (e0)) = (e2)) = ((e1) = (e2))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H7d. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_Hc8. % 8.45/8.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.70 cut (((op (e2) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 8.45/8.70 congruence. % 8.45/8.70 exact (zenon_Hca zenon_Hc9). % 8.45/8.70 apply zenon_H4b. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L44_ *) % 8.45/8.70 assert (zenon_L45_ : (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> False). % 8.45/8.70 do 0 intro. intros zenon_H6c zenon_Hcb zenon_Hcc. % 8.45/8.70 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (e1)) = (op (e1) (e1)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H6c. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_Hcb. % 8.45/8.70 cut (((e2) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hcd]. % 8.45/8.70 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H21. apply refl_equal. % 8.45/8.70 apply zenon_Hcd. apply sym_equal. exact zenon_Hcc. % 8.45/8.70 (* end of lemma zenon_L45_ *) % 8.45/8.70 assert (zenon_L46_ : ((op (e1) (e1)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e2))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H2a zenon_Hcc zenon_H7d. % 8.45/8.70 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H79 | zenon_intro zenon_H4b ]. % 8.45/8.70 cut (((e2) = (e2)) = ((e1) = (e2))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H7d. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H79. % 8.45/8.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.70 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hce]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e1) (e1)) = (e1)) = ((e2) = (e1))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Hce. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H2a. % 8.45/8.70 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.70 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 8.45/8.70 congruence. % 8.45/8.70 exact (zenon_Hcf zenon_Hcc). % 8.45/8.70 apply zenon_H40. apply refl_equal. % 8.45/8.70 apply zenon_H4b. apply refl_equal. % 8.45/8.70 apply zenon_H4b. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L46_ *) % 8.45/8.70 assert (zenon_L47_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> False). % 8.45/8.70 do 0 intro. intros zenon_Hd0 zenon_H30 zenon_Hd1. % 8.45/8.70 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Hd0. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H30. % 8.45/8.70 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 8.45/8.70 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H33. apply refl_equal. % 8.45/8.70 apply zenon_Hd2. apply sym_equal. exact zenon_Hd1. % 8.45/8.70 (* end of lemma zenon_L47_ *) % 8.45/8.70 assert (zenon_L48_ : (~((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 8.45/8.70 do 0 intro. intros zenon_Hd3 zenon_Hd4. % 8.45/8.70 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.45/8.70 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 8.45/8.70 congruence. % 8.45/8.70 exact (zenon_Hd5 zenon_Hd4). % 8.45/8.70 apply zenon_H58. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L48_ *) % 8.45/8.70 assert (zenon_L49_ : ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((e1) = (op (op (e3) (e3)) (e3)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_Hd6 zenon_Hd4 zenon_Hd7. % 8.45/8.70 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hd9 ]. % 8.45/8.70 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e1) = (op (op (e3) (e3)) (e3)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Hd7. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_Hd8. % 8.45/8.70 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 8.45/8.70 cut (((op (op (e3) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e0) (e3)) = (e1)) = ((op (op (e3) (e3)) (e3)) = (e1))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Hda. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_Hd6. % 8.45/8.70 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.70 cut (((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 8.45/8.70 congruence. % 8.45/8.70 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hd9 ]. % 8.45/8.70 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Hdb. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_Hd8. % 8.45/8.70 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 8.45/8.70 cut (((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 8.45/8.70 congruence. % 8.45/8.70 apply (zenon_L48_); trivial. % 8.45/8.70 apply zenon_Hd9. apply refl_equal. % 8.45/8.70 apply zenon_Hd9. apply refl_equal. % 8.45/8.70 apply zenon_H40. apply refl_equal. % 8.45/8.70 apply zenon_Hd9. apply refl_equal. % 8.45/8.70 apply zenon_Hd9. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L49_ *) % 8.45/8.70 assert (zenon_L50_ : ((op (e1) (e0)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> False). % 8.45/8.70 do 0 intro. intros zenon_Hb0 zenon_Hd6 zenon_Hd4. % 8.45/8.70 apply (zenon_notand_s _ _ ax11); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hdc ]. % 8.45/8.70 apply zenon_Hdd. apply sym_equal. exact zenon_Hd4. % 8.45/8.70 apply (zenon_notand_s _ _ zenon_Hdc); [ zenon_intro zenon_Hde | zenon_intro zenon_Hd7 ]. % 8.45/8.70 elim (classic ((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_Hdf | zenon_intro zenon_He0 ]. % 8.45/8.70 cut (((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3)))) = ((e2) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Hde. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_Hdf. % 8.45/8.70 cut (((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_He0]. % 8.45/8.70 cut (((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e1) (e0)) = (e2)) = ((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (e2))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_He1. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_Hb0. % 8.45/8.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.70 cut (((op (e1) (e0)) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_He2]. % 8.45/8.70 congruence. % 8.45/8.70 elim (classic ((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_Hdf | zenon_intro zenon_He0 ]. % 8.45/8.70 cut (((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3)))) = ((op (e1) (e0)) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_He2. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_Hdf. % 8.45/8.70 cut (((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_He0]. % 8.45/8.70 cut (((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_He3]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 8.45/8.70 cut (((op (op (e3) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e0) (e3)) = (e1)) = ((op (op (e3) (e3)) (e3)) = (e1))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Hda. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_Hd6. % 8.45/8.70 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.70 cut (((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 8.45/8.70 congruence. % 8.45/8.70 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hd9 ]. % 8.45/8.70 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Hdb. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_Hd8. % 8.45/8.70 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 8.45/8.70 cut (((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 8.45/8.70 congruence. % 8.45/8.70 apply (zenon_L48_); trivial. % 8.45/8.70 apply zenon_Hd9. apply refl_equal. % 8.45/8.70 apply zenon_Hd9. apply refl_equal. % 8.45/8.70 apply zenon_H40. apply refl_equal. % 8.45/8.70 exact (zenon_Hd5 zenon_Hd4). % 8.45/8.70 apply zenon_He0. apply refl_equal. % 8.45/8.70 apply zenon_He0. apply refl_equal. % 8.45/8.70 apply zenon_H4b. apply refl_equal. % 8.45/8.70 apply zenon_He0. apply refl_equal. % 8.45/8.70 apply zenon_He0. apply refl_equal. % 8.45/8.70 apply (zenon_L49_); trivial. % 8.45/8.70 (* end of lemma zenon_L50_ *) % 8.45/8.70 assert (zenon_L51_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 8.45/8.70 do 0 intro. intros zenon_He4 zenon_Hd6 zenon_He5. % 8.45/8.70 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_He4. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_Hd6. % 8.45/8.70 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He6]. % 8.45/8.70 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H33. apply refl_equal. % 8.45/8.70 apply zenon_He6. apply sym_equal. exact zenon_He5. % 8.45/8.70 (* end of lemma zenon_L51_ *) % 8.45/8.70 assert (zenon_L52_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e2)) -> False). % 8.45/8.70 do 0 intro. intros zenon_He7 zenon_H3c zenon_He8. % 8.45/8.70 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e3) (e3)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_He7. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H3c. % 8.45/8.70 cut (((e2) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He9]. % 8.45/8.70 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_Hea. apply refl_equal. % 8.45/8.70 apply zenon_He9. apply sym_equal. exact zenon_He8. % 8.45/8.70 (* end of lemma zenon_L52_ *) % 8.45/8.70 assert (zenon_L53_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> False). % 8.45/8.70 do 0 intro. intros zenon_Heb zenon_H98 zenon_H5a. % 8.45/8.70 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e3) (e3)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Heb. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H98. % 8.45/8.70 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 8.45/8.70 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H9c. apply refl_equal. % 8.45/8.70 apply zenon_Hec. apply sym_equal. exact zenon_H5a. % 8.45/8.70 (* end of lemma zenon_L53_ *) % 8.45/8.70 assert (zenon_L54_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.45/8.70 do 0 intro. intros zenon_Hed zenon_Hb0 zenon_Hd6 zenon_He4 zenon_H3c zenon_He7 zenon_Heb zenon_H98. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hee ]. % 8.45/8.70 apply (zenon_L50_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_He5 | zenon_intro zenon_Hef ]. % 8.45/8.70 apply (zenon_L51_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hef); [ zenon_intro zenon_He8 | zenon_intro zenon_H5a ]. % 8.45/8.70 apply (zenon_L52_); trivial. % 8.45/8.70 apply (zenon_L53_); trivial. % 8.45/8.70 (* end of lemma zenon_L54_ *) % 8.45/8.70 assert (zenon_L55_ : ((op (e3) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 8.45/8.70 do 0 intro. intros zenon_Hf0 zenon_Hf1 zenon_H7d. % 8.45/8.70 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H79 | zenon_intro zenon_H4b ]. % 8.45/8.70 cut (((e2) = (e2)) = ((e1) = (e2))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H7d. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H79. % 8.45/8.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.70 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hce]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e3) (e0)) = (e1)) = ((e2) = (e1))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Hce. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_Hf0. % 8.45/8.70 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.70 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 8.45/8.70 congruence. % 8.45/8.70 exact (zenon_Hf2 zenon_Hf1). % 8.45/8.70 apply zenon_H40. apply refl_equal. % 8.45/8.70 apply zenon_H4b. apply refl_equal. % 8.45/8.70 apply zenon_H4b. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L55_ *) % 8.45/8.70 assert (zenon_L56_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 8.45/8.70 do 0 intro. intros zenon_Hf3 zenon_H2a zenon_Hf4. % 8.45/8.70 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Hf3. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H2a. % 8.45/8.70 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 8.45/8.70 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H6e. apply refl_equal. % 8.45/8.70 apply zenon_Hf5. apply sym_equal. exact zenon_Hf4. % 8.45/8.70 (* end of lemma zenon_L56_ *) % 8.45/8.70 assert (zenon_L57_ : (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> False). % 8.45/8.70 do 0 intro. intros zenon_Ha3 zenon_H98 zenon_Hf6. % 8.45/8.70 cut (((op (e3) (e2)) = (e3)) = ((e1) = (e3))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Ha3. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H98. % 8.45/8.70 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.45/8.70 cut (((op (e3) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf7]. % 8.45/8.70 congruence. % 8.45/8.70 exact (zenon_Hf7 zenon_Hf6). % 8.45/8.70 apply zenon_H58. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L57_ *) % 8.45/8.70 assert (zenon_L58_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 8.45/8.70 do 0 intro. intros zenon_Hf8 zenon_H78 zenon_H1e zenon_Heb zenon_He7 zenon_H3c zenon_Hed zenon_Hc9 zenon_Hf9 zenon_H7d zenon_H2a zenon_Hf3 zenon_H98 zenon_Ha3 zenon_He4 zenon_Hd6. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.45/8.70 apply (zenon_L21_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.45/8.70 apply (zenon_L54_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.45/8.70 apply (zenon_L44_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hfc ]. % 8.45/8.70 apply (zenon_L55_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hfd ]. % 8.45/8.70 apply (zenon_L56_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_Hf6 | zenon_intro zenon_He5 ]. % 8.45/8.70 apply (zenon_L57_); trivial. % 8.45/8.70 apply (zenon_L51_); trivial. % 8.45/8.70 (* end of lemma zenon_L58_ *) % 8.45/8.70 assert (zenon_L59_ : ((op (e2) (e3)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H3c zenon_Hfe zenon_Hff. % 8.45/8.70 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H100 | zenon_intro zenon_Hea ]. % 8.45/8.70 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e0) (e3)) = (op (e2) (e3)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Hff. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H100. % 8.45/8.70 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 8.45/8.70 cut (((op (e2) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H101]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e0) (e3)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H101. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H3c. % 8.45/8.70 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 8.45/8.70 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_Hea. apply refl_equal. % 8.45/8.70 apply zenon_H102. apply sym_equal. exact zenon_Hfe. % 8.45/8.70 apply zenon_Hea. apply refl_equal. % 8.45/8.70 apply zenon_Hea. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L59_ *) % 8.45/8.70 assert (zenon_L60_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 8.45/8.70 do 0 intro. intros zenon_Hd0 zenon_H103 zenon_Hb3. % 8.45/8.70 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_Hd0. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H103. % 8.45/8.70 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H104]. % 8.45/8.70 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_H33. apply refl_equal. % 8.45/8.70 apply zenon_H104. apply sym_equal. exact zenon_Hb3. % 8.45/8.70 (* end of lemma zenon_L60_ *) % 8.45/8.70 assert (zenon_L61_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 8.45/8.70 do 0 intro. intros zenon_H105 zenon_Hd1 zenon_He4 zenon_Ha3 zenon_H98 zenon_Hf3 zenon_H2a zenon_H7d zenon_Hf9 zenon_Hc9 zenon_Hed zenon_He7 zenon_Heb zenon_H1e zenon_H78 zenon_Hf8 zenon_Hff zenon_H3c zenon_Hd0 zenon_Hb3. % 8.45/8.70 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H30 | zenon_intro zenon_H106 ]. % 8.45/8.70 apply (zenon_L47_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H107 ]. % 8.45/8.70 apply (zenon_L58_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfe | zenon_intro zenon_H103 ]. % 8.45/8.70 apply (zenon_L59_); trivial. % 8.45/8.70 apply (zenon_L60_); trivial. % 8.45/8.70 (* end of lemma zenon_L61_ *) % 8.45/8.70 assert (zenon_L62_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_Hba zenon_H9a zenon_H94 zenon_H90 zenon_H71 zenon_H9f zenon_Ha8 zenon_H93 zenon_H105 zenon_Hd1 zenon_He4 zenon_Ha3 zenon_H98 zenon_Hf3 zenon_H2a zenon_H7d zenon_Hf9 zenon_Hc9 zenon_Hed zenon_He7 zenon_Heb zenon_H1e zenon_H78 zenon_Hf8 zenon_Hff zenon_H3c zenon_Hd0. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.45/8.70 apply (zenon_L30_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.45/8.70 apply (zenon_L31_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.45/8.70 apply (zenon_L32_); trivial. % 8.45/8.70 apply (zenon_L61_); trivial. % 8.45/8.70 (* end of lemma zenon_L62_ *) % 8.45/8.70 assert (zenon_L63_ : ((op (e2) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H3c zenon_H108 zenon_H109. % 8.45/8.70 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H100 | zenon_intro zenon_Hea ]. % 8.45/8.70 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e1) (e3)) = (op (e2) (e3)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H109. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H100. % 8.45/8.70 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 8.45/8.70 cut (((op (e2) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 8.45/8.70 congruence. % 8.45/8.70 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e1) (e3)))). % 8.45/8.70 intro zenon_D_pnotp. % 8.45/8.70 apply zenon_H10a. % 8.45/8.70 rewrite <- zenon_D_pnotp. % 8.45/8.70 exact zenon_H3c. % 8.45/8.70 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10b]. % 8.45/8.70 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 8.45/8.70 congruence. % 8.45/8.70 apply zenon_Hea. apply refl_equal. % 8.45/8.70 apply zenon_H10b. apply sym_equal. exact zenon_H108. % 8.45/8.70 apply zenon_Hea. apply refl_equal. % 8.45/8.70 apply zenon_Hea. apply refl_equal. % 8.45/8.70 (* end of lemma zenon_L63_ *) % 8.45/8.70 assert (zenon_L64_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 8.45/8.70 do 0 intro. intros zenon_H10c zenon_Hc2 zenon_Hbf zenon_Hab zenon_Hb4 zenon_H74 zenon_Hb7 zenon_H3a zenon_H67 zenon_Hc5 zenon_Hd0 zenon_Hff zenon_Hf8 zenon_H78 zenon_H1e zenon_Heb zenon_He7 zenon_Hed zenon_Hc9 zenon_Hf9 zenon_H7d zenon_H2a zenon_Hf3 zenon_H98 zenon_Ha3 zenon_He4 zenon_Hd1 zenon_H105 zenon_Ha8 zenon_H9f zenon_H71 zenon_H90 zenon_H94 zenon_H9a zenon_Hba zenon_H3c zenon_H109. % 8.45/8.70 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.45/8.70 apply (zenon_L43_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.45/8.70 apply (zenon_L46_); trivial. % 8.45/8.70 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.45/8.70 apply (zenon_L62_); trivial. % 8.45/8.70 apply (zenon_L63_); trivial. % 8.45/8.70 (* end of lemma zenon_L64_ *) % 8.45/8.70 assert (zenon_L65_ : (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e0)) -> False). % 8.45/8.70 do 0 intro. intros zenon_H78 zenon_H3c zenon_H10f. % 8.45/8.70 cut (((op (e2) (e3)) = (e2)) = ((e0) = (e2))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H78. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H3c. % 8.45/8.71 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.71 cut (((op (e2) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 8.45/8.71 congruence. % 8.45/8.71 exact (zenon_H110 zenon_H10f). % 8.45/8.71 apply zenon_H4b. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L65_ *) % 8.45/8.71 assert (zenon_L66_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 8.45/8.71 do 0 intro. intros zenon_He4 zenon_H30 zenon_Hd4. % 8.45/8.71 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_He4. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H30. % 8.45/8.71 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hdd]. % 8.45/8.71 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H33. apply refl_equal. % 8.45/8.71 apply zenon_Hdd. apply sym_equal. exact zenon_Hd4. % 8.45/8.71 (* end of lemma zenon_L66_ *) % 8.45/8.71 assert (zenon_L67_ : ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> (~((e2) = (op (op (e3) (e3)) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_Hfe zenon_Hd4 zenon_H111. % 8.45/8.71 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hd9 ]. % 8.45/8.71 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e2) = (op (op (e3) (e3)) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H111. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Hd8. % 8.45/8.71 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 8.45/8.71 cut (((op (op (e3) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e0) (e3)) = (e2)) = ((op (op (e3) (e3)) (e3)) = (e2))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H112. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Hfe. % 8.45/8.71 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.71 cut (((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 8.45/8.71 congruence. % 8.45/8.71 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hd9 ]. % 8.45/8.71 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_Hdb. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Hd8. % 8.45/8.71 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 8.45/8.71 cut (((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 8.45/8.71 congruence. % 8.45/8.71 apply (zenon_L48_); trivial. % 8.45/8.71 apply zenon_Hd9. apply refl_equal. % 8.45/8.71 apply zenon_Hd9. apply refl_equal. % 8.45/8.71 apply zenon_H4b. apply refl_equal. % 8.45/8.71 apply zenon_Hd9. apply refl_equal. % 8.45/8.71 apply zenon_Hd9. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L67_ *) % 8.45/8.71 assert (zenon_L68_ : ((op (e2) (e0)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> False). % 8.45/8.71 do 0 intro. intros zenon_Hc9 zenon_Hfe zenon_Hd4. % 8.45/8.71 apply (zenon_notand_s _ _ ax10); [ zenon_intro zenon_Hdd | zenon_intro zenon_H113 ]. % 8.45/8.71 apply zenon_Hdd. apply sym_equal. exact zenon_Hd4. % 8.45/8.71 apply (zenon_notand_s _ _ zenon_H113); [ zenon_intro zenon_H114 | zenon_intro zenon_H111 ]. % 8.45/8.71 elim (classic ((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_Hdf | zenon_intro zenon_He0 ]. % 8.45/8.71 cut (((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3)))) = ((e1) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H114. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Hdf. % 8.45/8.71 cut (((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_He0]. % 8.45/8.71 cut (((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e2) (e0)) = (e1)) = ((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (e1))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H115. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Hc9. % 8.45/8.71 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.71 cut (((op (e2) (e0)) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 8.45/8.71 congruence. % 8.45/8.71 elim (classic ((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_Hdf | zenon_intro zenon_He0 ]. % 8.45/8.71 cut (((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3)))) = ((op (e2) (e0)) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H116. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Hdf. % 8.45/8.71 cut (((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_He0]. % 8.45/8.71 cut (((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H117]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 8.45/8.71 cut (((op (op (e3) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e0) (e3)) = (e2)) = ((op (op (e3) (e3)) (e3)) = (e2))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H112. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Hfe. % 8.45/8.71 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.71 cut (((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 8.45/8.71 congruence. % 8.45/8.71 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hd9 ]. % 8.45/8.71 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_Hdb. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Hd8. % 8.45/8.71 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 8.45/8.71 cut (((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 8.45/8.71 congruence. % 8.45/8.71 apply (zenon_L48_); trivial. % 8.45/8.71 apply zenon_Hd9. apply refl_equal. % 8.45/8.71 apply zenon_Hd9. apply refl_equal. % 8.45/8.71 apply zenon_H4b. apply refl_equal. % 8.45/8.71 exact (zenon_Hd5 zenon_Hd4). % 8.45/8.71 apply zenon_He0. apply refl_equal. % 8.45/8.71 apply zenon_He0. apply refl_equal. % 8.45/8.71 apply zenon_H40. apply refl_equal. % 8.45/8.71 apply zenon_He0. apply refl_equal. % 8.45/8.71 apply zenon_He0. apply refl_equal. % 8.45/8.71 apply (zenon_L67_); trivial. % 8.45/8.71 (* end of lemma zenon_L68_ *) % 8.45/8.71 assert (zenon_L69_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_Hf9 zenon_H7d zenon_Hf1 zenon_H2a zenon_Hf3 zenon_H98 zenon_Ha3 zenon_H105 zenon_He4 zenon_Hd4 zenon_Hc9 zenon_Hd0 zenon_Hb3. % 8.45/8.71 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hfc ]. % 8.45/8.71 apply (zenon_L55_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hfd ]. % 8.45/8.71 apply (zenon_L56_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_Hf6 | zenon_intro zenon_He5 ]. % 8.45/8.71 apply (zenon_L57_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H30 | zenon_intro zenon_H106 ]. % 8.45/8.71 apply (zenon_L66_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H107 ]. % 8.45/8.71 apply (zenon_L51_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfe | zenon_intro zenon_H103 ]. % 8.45/8.71 apply (zenon_L68_); trivial. % 8.45/8.71 apply (zenon_L60_); trivial. % 8.45/8.71 (* end of lemma zenon_L69_ *) % 8.45/8.71 assert (zenon_L70_ : (~((op (e0) (op (e0) (e2))) = (e2))) -> ((op (e0) (e2)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H118 zenon_H7e. % 8.45/8.71 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (op (e0) (e2))) = (e2))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H118. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H7e. % 8.45/8.71 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.71 cut (((op (e0) (e2)) = (op (e0) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 8.45/8.71 congruence. % 8.45/8.71 elim (classic ((op (e0) (op (e0) (e2))) = (op (e0) (op (e0) (e2))))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 8.45/8.71 cut (((op (e0) (op (e0) (e2))) = (op (e0) (op (e0) (e2)))) = ((op (e0) (e2)) = (op (e0) (op (e0) (e2))))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H119. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H11a. % 8.45/8.71 cut (((op (e0) (op (e0) (e2))) = (op (e0) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 8.45/8.71 cut (((op (e0) (op (e0) (e2))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e0) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H11d]. % 8.45/8.71 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H3f. apply refl_equal. % 8.45/8.71 exact (zenon_H11d zenon_H7e). % 8.45/8.71 apply zenon_H11b. apply refl_equal. % 8.45/8.71 apply zenon_H11b. apply refl_equal. % 8.45/8.71 apply zenon_H4b. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L70_ *) % 8.45/8.71 assert (zenon_L71_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (op (e0) (e2))) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H11e zenon_H109 zenon_H11f zenon_H31 zenon_Hba zenon_H9a zenon_H94 zenon_H90 zenon_H71 zenon_H9f zenon_Ha8 zenon_Hed zenon_He7 zenon_Heb zenon_H1e zenon_Hf8 zenon_Hc5 zenon_H67 zenon_H3a zenon_Hb7 zenon_H74 zenon_Hb4 zenon_Hab zenon_Hbf zenon_Hc2 zenon_H10c zenon_H78 zenon_Hf9 zenon_H7d zenon_H2a zenon_Hf3 zenon_H98 zenon_Ha3 zenon_H105 zenon_He4 zenon_Hc9 zenon_Hd0 zenon_H6c zenon_H118 zenon_H3c zenon_Hff. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.45/8.71 apply (zenon_L21_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.45/8.71 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.45/8.71 apply (zenon_L21_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.45/8.71 apply (zenon_L43_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.45/8.71 apply (zenon_L44_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.45/8.71 apply (zenon_L43_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.45/8.71 apply (zenon_L45_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.45/8.71 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.45/8.71 apply (zenon_L30_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.45/8.71 apply (zenon_L31_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.45/8.71 apply (zenon_L32_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.45/8.71 apply (zenon_L4_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.45/8.71 apply (zenon_L64_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.45/8.71 apply (zenon_L65_); trivial. % 8.45/8.71 apply (zenon_L69_); trivial. % 8.45/8.71 apply (zenon_L63_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.45/8.71 apply (zenon_L70_); trivial. % 8.45/8.71 apply (zenon_L59_); trivial. % 8.45/8.71 (* end of lemma zenon_L71_ *) % 8.45/8.71 assert (zenon_L72_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H24 zenon_H1d zenon_H124. % 8.45/8.71 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H26 | zenon_intro zenon_H27 ]. % 8.45/8.71 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e1)) = (op (e0) (e2)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H124. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H26. % 8.45/8.71 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 8.45/8.71 cut (((op (e0) (e2)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H125]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e0) (e1)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H125. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H24. % 8.45/8.71 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H126]. % 8.45/8.71 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H27. apply refl_equal. % 8.45/8.71 apply zenon_H126. apply sym_equal. exact zenon_H1d. % 8.45/8.71 apply zenon_H27. apply refl_equal. % 8.45/8.71 apply zenon_H27. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L72_ *) % 8.45/8.71 assert (zenon_L73_ : (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H127 zenon_H1d zenon_H30. % 8.45/8.71 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e0) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H127. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H1d. % 8.45/8.71 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H128]. % 8.45/8.71 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H21. apply refl_equal. % 8.45/8.71 apply zenon_H128. apply sym_equal. exact zenon_H30. % 8.45/8.71 (* end of lemma zenon_L73_ *) % 8.45/8.71 assert (zenon_L74_ : (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H129 zenon_H29 zenon_H35. % 8.45/8.71 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e1) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H129. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H29. % 8.45/8.71 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12a]. % 8.45/8.71 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H2d. apply refl_equal. % 8.45/8.71 apply zenon_H12a. apply sym_equal. exact zenon_H35. % 8.45/8.71 (* end of lemma zenon_L74_ *) % 8.45/8.71 assert (zenon_L75_ : ((op (e2) (e3)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H3c zenon_Hc8 zenon_H12b. % 8.45/8.71 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H100 | zenon_intro zenon_Hea ]. % 8.45/8.71 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e0)) = (op (e2) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H12b. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H100. % 8.45/8.71 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 8.45/8.71 cut (((op (e2) (e3)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e2) (e0)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H12c. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H3c. % 8.45/8.71 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 8.45/8.71 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_Hea. apply refl_equal. % 8.45/8.71 apply zenon_H12d. apply sym_equal. exact zenon_Hc8. % 8.45/8.71 apply zenon_Hea. apply refl_equal. % 8.45/8.71 apply zenon_Hea. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L75_ *) % 8.45/8.71 assert (zenon_L76_ : (~((op (e0) (op (e0) (e0))) = (e0))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e0)) = (e1)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H12e zenon_H1d zenon_H66. % 8.45/8.71 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (op (e0) (e0))) = (e0))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H12e. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H1d. % 8.45/8.71 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.45/8.71 cut (((op (e0) (e1)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H12f]. % 8.45/8.71 congruence. % 8.45/8.71 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H130 | zenon_intro zenon_H131 ]. % 8.45/8.71 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e1)) = (op (e0) (op (e0) (e0))))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H12f. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H130. % 8.45/8.71 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 8.45/8.71 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 8.45/8.71 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H3f. apply refl_equal. % 8.45/8.71 exact (zenon_H6a zenon_H66). % 8.45/8.71 apply zenon_H131. apply refl_equal. % 8.45/8.71 apply zenon_H131. apply refl_equal. % 8.45/8.71 apply zenon_H3f. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L76_ *) % 8.45/8.71 assert (zenon_L77_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1d zenon_H6b zenon_H67. % 8.45/8.71 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H68 | zenon_intro zenon_H40 ]. % 8.45/8.71 cut (((e1) = (e1)) = ((e0) = (e1))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H67. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H68. % 8.45/8.71 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.71 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e0) (e1)) = (e0)) = ((e1) = (e0))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H69. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H1d. % 8.45/8.71 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.45/8.71 cut (((op (e0) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 8.45/8.71 congruence. % 8.45/8.71 exact (zenon_H133 zenon_H6b). % 8.45/8.71 apply zenon_H3f. apply refl_equal. % 8.45/8.71 apply zenon_H40. apply refl_equal. % 8.45/8.71 apply zenon_H40. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L77_ *) % 8.45/8.71 assert (zenon_L78_ : ((op (e1) (e2)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H29 zenon_H71 zenon_H134. % 8.45/8.71 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H2c | zenon_intro zenon_H2d ]. % 8.45/8.71 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e0) (e2)) = (op (e1) (e2)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H134. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H2c. % 8.45/8.71 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 8.45/8.71 cut (((op (e1) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e0) (e2)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H135. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H29. % 8.45/8.71 cut (((e1) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 8.45/8.71 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H2d. apply refl_equal. % 8.45/8.71 apply zenon_H136. apply sym_equal. exact zenon_H71. % 8.45/8.71 apply zenon_H2d. apply refl_equal. % 8.45/8.71 apply zenon_H2d. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L78_ *) % 8.45/8.71 assert (zenon_L79_ : ((op (e2) (e0)) = (e2)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_Hc8 zenon_H77 zenon_H137. % 8.45/8.71 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 8.45/8.71 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e0) (e0)) = (op (e2) (e0)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H137. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H138. % 8.45/8.71 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 8.45/8.71 cut (((op (e2) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e0) (e0)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H13a. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Hc8. % 8.45/8.71 cut (((e2) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 8.45/8.71 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H139. apply refl_equal. % 8.45/8.71 apply zenon_H13b. apply sym_equal. exact zenon_H77. % 8.45/8.71 apply zenon_H139. apply refl_equal. % 8.45/8.71 apply zenon_H139. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L79_ *) % 8.45/8.71 assert (zenon_L80_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1d zenon_Hcb zenon_H78. % 8.45/8.71 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H79 | zenon_intro zenon_H4b ]. % 8.45/8.71 cut (((e2) = (e2)) = ((e0) = (e2))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H78. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H79. % 8.45/8.71 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.71 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e0) (e1)) = (e0)) = ((e2) = (e0))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H7a. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H1d. % 8.45/8.71 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.45/8.71 cut (((op (e0) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H13c]. % 8.45/8.71 congruence. % 8.45/8.71 exact (zenon_H13c zenon_Hcb). % 8.45/8.71 apply zenon_H3f. apply refl_equal. % 8.45/8.71 apply zenon_H4b. apply refl_equal. % 8.45/8.71 apply zenon_H4b. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L80_ *) % 8.45/8.71 assert (zenon_L81_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 8.45/8.71 do 0 intro. intros zenon_Hd6 zenon_Hfe zenon_H7d. % 8.45/8.71 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H79 | zenon_intro zenon_H4b ]. % 8.45/8.71 cut (((e2) = (e2)) = ((e1) = (e2))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H7d. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H79. % 8.45/8.71 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.71 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hce]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e0) (e3)) = (e1)) = ((e2) = (e1))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_Hce. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Hd6. % 8.45/8.71 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.71 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H13d]. % 8.45/8.71 congruence. % 8.45/8.71 exact (zenon_H13d zenon_Hfe). % 8.45/8.71 apply zenon_H40. apply refl_equal. % 8.45/8.71 apply zenon_H4b. apply refl_equal. % 8.45/8.71 apply zenon_H4b. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L81_ *) % 8.45/8.71 assert (zenon_L82_ : (~((op (e1) (op (e1) (e0))) = (e0))) -> ((op (e1) (e0)) = (e0)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H49 zenon_Hac. % 8.45/8.71 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (op (e1) (e0))) = (e0))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H49. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Hac. % 8.45/8.71 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.45/8.71 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H13e]. % 8.45/8.71 congruence. % 8.45/8.71 elim (classic ((op (e1) (op (e1) (e0))) = (op (e1) (op (e1) (e0))))); [ zenon_intro zenon_H13f | zenon_intro zenon_H140 ]. % 8.45/8.71 cut (((op (e1) (op (e1) (e0))) = (op (e1) (op (e1) (e0)))) = ((op (e1) (e0)) = (op (e1) (op (e1) (e0))))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H13e. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H13f. % 8.45/8.71 cut (((op (e1) (op (e1) (e0))) = (op (e1) (op (e1) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 8.45/8.71 cut (((op (e1) (op (e1) (e0))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e1) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H142]. % 8.45/8.71 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H40. apply refl_equal. % 8.45/8.71 exact (zenon_H142 zenon_Hac). % 8.45/8.71 apply zenon_H140. apply refl_equal. % 8.45/8.71 apply zenon_H140. apply refl_equal. % 8.45/8.71 apply zenon_H3f. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L82_ *) % 8.45/8.71 assert (zenon_L83_ : (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e0)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H78 zenon_Hc8 zenon_H143. % 8.45/8.71 cut (((op (e2) (e0)) = (e2)) = ((e0) = (e2))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H78. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Hc8. % 8.45/8.71 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.71 cut (((op (e2) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H144]. % 8.45/8.71 congruence. % 8.45/8.71 exact (zenon_H144 zenon_H143). % 8.45/8.71 apply zenon_H4b. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L83_ *) % 8.45/8.71 assert (zenon_L84_ : ((op (e2) (e0)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_Hc8 zenon_Hb0 zenon_H145. % 8.45/8.71 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 8.45/8.71 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e1) (e0)) = (op (e2) (e0)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H145. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H138. % 8.45/8.71 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 8.45/8.71 cut (((op (e2) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e1) (e0)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H146. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Hc8. % 8.45/8.71 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 8.45/8.71 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H139. apply refl_equal. % 8.45/8.71 apply zenon_Hb2. apply sym_equal. exact zenon_Hb0. % 8.45/8.71 apply zenon_H139. apply refl_equal. % 8.45/8.71 apply zenon_H139. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L84_ *) % 8.45/8.71 assert (zenon_L85_ : (~((op (e1) (op (e1) (e1))) = (e1))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H41 zenon_H29 zenon_Hcc. % 8.45/8.71 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (op (e1) (e1))) = (e1))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H41. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H29. % 8.45/8.71 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.71 cut (((op (e1) (e2)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H147]. % 8.45/8.71 congruence. % 8.45/8.71 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_H43 | zenon_intro zenon_H44 ]. % 8.45/8.71 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e2)) = (op (e1) (op (e1) (e1))))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H147. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H43. % 8.45/8.71 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 8.45/8.71 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H148]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 8.45/8.71 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H40. apply refl_equal. % 8.45/8.71 exact (zenon_Hcf zenon_Hcc). % 8.45/8.71 apply zenon_H44. apply refl_equal. % 8.45/8.71 apply zenon_H44. apply refl_equal. % 8.45/8.71 apply zenon_H40. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L85_ *) % 8.45/8.71 assert (zenon_L86_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H134 zenon_H7e zenon_H93. % 8.45/8.71 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H134. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H7e. % 8.45/8.71 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 8.45/8.71 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H27. apply refl_equal. % 8.45/8.71 apply zenon_H97. apply sym_equal. exact zenon_H93. % 8.45/8.71 (* end of lemma zenon_L86_ *) % 8.45/8.71 assert (zenon_L87_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_Hd6 zenon_H66 zenon_H31. % 8.45/8.71 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H32 | zenon_intro zenon_H33 ]. % 8.45/8.71 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e0)) = (op (e0) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H31. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H32. % 8.45/8.71 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 8.45/8.71 cut (((op (e0) (e3)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e0) (e0)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H34. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Hd6. % 8.45/8.71 cut (((e1) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 8.45/8.71 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H33. apply refl_equal. % 8.45/8.71 apply zenon_H72. apply sym_equal. exact zenon_H66. % 8.45/8.71 apply zenon_H33. apply refl_equal. % 8.45/8.71 apply zenon_H33. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L87_ *) % 8.45/8.71 assert (zenon_L88_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_Hd0 zenon_Hfe zenon_H108. % 8.45/8.71 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_Hd0. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Hfe. % 8.45/8.71 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10b]. % 8.45/8.71 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H33. apply refl_equal. % 8.45/8.71 apply zenon_H10b. apply sym_equal. exact zenon_H108. % 8.45/8.71 (* end of lemma zenon_L88_ *) % 8.45/8.71 assert (zenon_L89_ : ((op (e3) (e3)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H5a zenon_H103 zenon_He4. % 8.45/8.71 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 8.45/8.71 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_He4. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H149. % 8.45/8.71 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 8.45/8.71 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H14b]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H14b. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H5a. % 8.45/8.71 cut (((e3) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 8.45/8.71 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H14a. apply refl_equal. % 8.45/8.71 apply zenon_H14c. apply sym_equal. exact zenon_H103. % 8.45/8.71 apply zenon_H14a. apply refl_equal. % 8.45/8.71 apply zenon_H14a. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L89_ *) % 8.45/8.71 assert (zenon_L90_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H10c zenon_H145 zenon_Hc8 zenon_H29 zenon_H41 zenon_H7e zenon_H134 zenon_H105 zenon_Hd1 zenon_H31 zenon_H66 zenon_Hd0 zenon_H5a zenon_He4. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.45/8.71 apply (zenon_L84_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.45/8.71 apply (zenon_L85_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.45/8.71 apply (zenon_L86_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H30 | zenon_intro zenon_H106 ]. % 8.45/8.71 apply (zenon_L47_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H107 ]. % 8.45/8.71 apply (zenon_L87_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfe | zenon_intro zenon_H103 ]. % 8.45/8.71 apply (zenon_L88_); trivial. % 8.45/8.71 apply (zenon_L89_); trivial. % 8.45/8.71 (* end of lemma zenon_L90_ *) % 8.45/8.71 assert (zenon_L91_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 8.45/8.71 do 0 intro. intros zenon_Hff zenon_H30 zenon_H10f. % 8.45/8.71 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_Hff. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H30. % 8.45/8.71 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 8.45/8.71 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H33. apply refl_equal. % 8.45/8.71 apply zenon_H14d. apply sym_equal. exact zenon_H10f. % 8.45/8.71 (* end of lemma zenon_L91_ *) % 8.45/8.71 assert (zenon_L92_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H105 zenon_H10f zenon_Hff zenon_H31 zenon_H66 zenon_H108 zenon_Hd0 zenon_H5a zenon_He4. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H30 | zenon_intro zenon_H106 ]. % 8.45/8.71 apply (zenon_L91_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H107 ]. % 8.45/8.71 apply (zenon_L87_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfe | zenon_intro zenon_H103 ]. % 8.45/8.71 apply (zenon_L88_); trivial. % 8.45/8.71 apply (zenon_L89_); trivial. % 8.45/8.71 (* end of lemma zenon_L92_ *) % 8.45/8.71 assert (zenon_L93_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H29 zenon_H73 zenon_Hab. % 8.45/8.71 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H2c | zenon_intro zenon_H2d ]. % 8.45/8.71 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e0)) = (op (e1) (e2)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_Hab. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H2c. % 8.45/8.71 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 8.45/8.71 cut (((op (e1) (e2)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e1) (e0)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_Hb1. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H29. % 8.45/8.71 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 8.45/8.71 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H2d. apply refl_equal. % 8.45/8.71 apply zenon_H76. apply sym_equal. exact zenon_H73. % 8.45/8.71 apply zenon_H2d. apply refl_equal. % 8.45/8.71 apply zenon_H2d. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L93_ *) % 8.45/8.71 assert (zenon_L94_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H14e zenon_Hf0 zenon_H67. % 8.45/8.71 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H68 | zenon_intro zenon_H40 ]. % 8.45/8.71 cut (((e1) = (e1)) = ((e0) = (e1))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H67. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H68. % 8.45/8.71 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.71 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e3) (e0)) = (e0)) = ((e1) = (e0))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H69. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H14e. % 8.45/8.71 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.45/8.71 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 8.45/8.71 congruence. % 8.45/8.71 exact (zenon_H14f zenon_Hf0). % 8.45/8.71 apply zenon_H3f. apply refl_equal. % 8.45/8.71 apply zenon_H40. apply refl_equal. % 8.45/8.71 apply zenon_H40. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L94_ *) % 8.45/8.71 assert (zenon_L95_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H150 zenon_H31 zenon_Hd6 zenon_Hab zenon_H29 zenon_Hc8 zenon_H7d zenon_H14e zenon_H67. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.45/8.71 apply (zenon_L87_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.45/8.71 apply (zenon_L93_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.45/8.71 apply (zenon_L44_); trivial. % 8.45/8.71 apply (zenon_L94_); trivial. % 8.45/8.71 (* end of lemma zenon_L95_ *) % 8.45/8.71 assert (zenon_L96_ : (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H153 zenon_H7e zenon_Hfe. % 8.45/8.71 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e0) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H153. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H7e. % 8.45/8.71 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 8.45/8.71 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H27. apply refl_equal. % 8.45/8.71 apply zenon_H102. apply sym_equal. exact zenon_Hfe. % 8.45/8.71 (* end of lemma zenon_L96_ *) % 8.45/8.71 assert (zenon_L97_ : (~((op (e1) (op (e1) (e2))) = (e2))) -> ((op (e1) (e2)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H154 zenon_H93. % 8.45/8.71 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (op (e1) (e2))) = (e2))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H154. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H93. % 8.45/8.71 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.71 cut (((op (e1) (e2)) = (op (e1) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 8.45/8.71 congruence. % 8.45/8.71 elim (classic ((op (e1) (op (e1) (e2))) = (op (e1) (op (e1) (e2))))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ]. % 8.45/8.71 cut (((op (e1) (op (e1) (e2))) = (op (e1) (op (e1) (e2)))) = ((op (e1) (e2)) = (op (e1) (op (e1) (e2))))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H155. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H156. % 8.45/8.71 cut (((op (e1) (op (e1) (e2))) = (op (e1) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H157]. % 8.45/8.71 cut (((op (e1) (op (e1) (e2))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H158]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e1) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 8.45/8.71 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H40. apply refl_equal. % 8.45/8.71 exact (zenon_H159 zenon_H93). % 8.45/8.71 apply zenon_H157. apply refl_equal. % 8.45/8.71 apply zenon_H157. apply refl_equal. % 8.45/8.71 apply zenon_H4b. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L97_ *) % 8.45/8.71 assert (zenon_L98_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H10c zenon_H145 zenon_Hc8 zenon_H29 zenon_H41 zenon_H154 zenon_Hd0 zenon_Hfe. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.45/8.71 apply (zenon_L84_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.45/8.71 apply (zenon_L85_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.45/8.71 apply (zenon_L97_); trivial. % 8.45/8.71 apply (zenon_L88_); trivial. % 8.45/8.71 (* end of lemma zenon_L98_ *) % 8.45/8.71 assert (zenon_L99_ : (~((op (e2) (op (e2) (e1))) = (e1))) -> ((op (e2) (e1)) = (e1)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H56 zenon_H15a. % 8.45/8.71 cut (((op (e2) (e1)) = (e1)) = ((op (e2) (op (e2) (e1))) = (e1))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H56. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H15a. % 8.45/8.71 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.71 cut (((op (e2) (e1)) = (op (e2) (op (e2) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 8.45/8.71 congruence. % 8.45/8.71 elim (classic ((op (e2) (op (e2) (e1))) = (op (e2) (op (e2) (e1))))); [ zenon_intro zenon_H15c | zenon_intro zenon_H15d ]. % 8.45/8.71 cut (((op (e2) (op (e2) (e1))) = (op (e2) (op (e2) (e1)))) = ((op (e2) (e1)) = (op (e2) (op (e2) (e1))))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H15b. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H15c. % 8.45/8.71 cut (((op (e2) (op (e2) (e1))) = (op (e2) (op (e2) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H15d]. % 8.45/8.71 cut (((op (e2) (op (e2) (e1))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H15e]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e2) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H15f]. % 8.45/8.71 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H4b. apply refl_equal. % 8.45/8.71 exact (zenon_H15f zenon_H15a). % 8.45/8.71 apply zenon_H15d. apply refl_equal. % 8.45/8.71 apply zenon_H15d. apply refl_equal. % 8.45/8.71 apply zenon_H40. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L99_ *) % 8.45/8.71 assert (zenon_L100_ : (~((op (e2) (op (e2) (e0))) = (e0))) -> ((op (e2) (e0)) = (e0)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H54 zenon_H143. % 8.45/8.71 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (op (e2) (e0))) = (e0))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H54. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H143. % 8.45/8.71 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.45/8.71 cut (((op (e2) (e0)) = (op (e2) (op (e2) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H160]. % 8.45/8.71 congruence. % 8.45/8.71 elim (classic ((op (e2) (op (e2) (e0))) = (op (e2) (op (e2) (e0))))); [ zenon_intro zenon_H161 | zenon_intro zenon_H162 ]. % 8.45/8.71 cut (((op (e2) (op (e2) (e0))) = (op (e2) (op (e2) (e0)))) = ((op (e2) (e0)) = (op (e2) (op (e2) (e0))))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H160. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H161. % 8.45/8.71 cut (((op (e2) (op (e2) (e0))) = (op (e2) (op (e2) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 8.45/8.71 cut (((op (e2) (op (e2) (e0))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H163]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e2) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H144]. % 8.45/8.71 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H4b. apply refl_equal. % 8.45/8.71 exact (zenon_H144 zenon_H143). % 8.45/8.71 apply zenon_H162. apply refl_equal. % 8.45/8.71 apply zenon_H162. apply refl_equal. % 8.45/8.71 apply zenon_H3f. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L100_ *) % 8.45/8.71 assert (zenon_L101_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H164 zenon_H1d zenon_H165. % 8.45/8.71 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H164. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H1d. % 8.45/8.71 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H166]. % 8.45/8.71 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H21. apply refl_equal. % 8.45/8.71 apply zenon_H166. apply sym_equal. exact zenon_H165. % 8.45/8.71 (* end of lemma zenon_L101_ *) % 8.45/8.71 assert (zenon_L102_ : (~((op (e2) (op (e2) (e2))) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H4c zenon_Hc8 zenon_H80. % 8.45/8.71 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (op (e2) (e2))) = (e2))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H4c. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Hc8. % 8.45/8.71 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.71 cut (((op (e2) (e0)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 8.45/8.71 congruence. % 8.45/8.71 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H4e | zenon_intro zenon_H4f ]. % 8.45/8.71 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((op (e2) (e0)) = (op (e2) (op (e2) (e2))))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H167. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H4e. % 8.45/8.71 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 8.45/8.71 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 8.45/8.71 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H4b. apply refl_equal. % 8.45/8.71 exact (zenon_H81 zenon_H80). % 8.45/8.71 apply zenon_H4f. apply refl_equal. % 8.45/8.71 apply zenon_H4f. apply refl_equal. % 8.45/8.71 apply zenon_H4b. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L102_ *) % 8.45/8.71 assert (zenon_L103_ : (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H169 zenon_H15a zenon_Hf4. % 8.45/8.71 cut (((op (e2) (e1)) = (e1)) = ((op (e2) (e1)) = (op (e3) (e1)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H169. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H15a. % 8.45/8.71 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 8.45/8.71 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H16a. apply refl_equal. % 8.45/8.71 apply zenon_Hf5. apply sym_equal. exact zenon_Hf4. % 8.45/8.71 (* end of lemma zenon_L103_ *) % 8.45/8.71 assert (zenon_L104_ : (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H94 zenon_H29 zenon_H91. % 8.45/8.71 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e2) (e2)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H94. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H29. % 8.45/8.71 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H92]. % 8.45/8.71 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H2d. apply refl_equal. % 8.45/8.71 apply zenon_H92. apply sym_equal. exact zenon_H91. % 8.45/8.71 (* end of lemma zenon_L104_ *) % 8.45/8.71 assert (zenon_L105_ : (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> False). % 8.45/8.71 do 0 intro. intros zenon_Hb4 zenon_Hac zenon_Hd1. % 8.45/8.71 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (e0)) = (op (e1) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_Hb4. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Hac. % 8.45/8.71 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 8.45/8.71 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_Haf. apply refl_equal. % 8.45/8.71 apply zenon_Hd2. apply sym_equal. exact zenon_Hd1. % 8.45/8.71 (* end of lemma zenon_L105_ *) % 8.45/8.71 assert (zenon_L106_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H109 zenon_H35 zenon_H16b. % 8.45/8.71 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H109. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H35. % 8.45/8.71 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 8.45/8.71 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H38. apply refl_equal. % 8.45/8.71 apply zenon_H16c. apply sym_equal. exact zenon_H16b. % 8.45/8.71 (* end of lemma zenon_L106_ *) % 8.45/8.71 assert (zenon_L107_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 8.45/8.71 do 0 intro. intros zenon_Hff zenon_Hd6 zenon_H16b. % 8.45/8.71 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_Hff. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Hd6. % 8.45/8.71 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 8.45/8.71 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H33. apply refl_equal. % 8.45/8.71 apply zenon_H16c. apply sym_equal. exact zenon_H16b. % 8.45/8.71 (* end of lemma zenon_L107_ *) % 8.45/8.71 assert (zenon_L108_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H105 zenon_H10f zenon_H16b zenon_Hff zenon_H108 zenon_Hd0 zenon_H5a zenon_He4. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H30 | zenon_intro zenon_H106 ]. % 8.45/8.71 apply (zenon_L91_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H107 ]. % 8.45/8.71 apply (zenon_L107_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfe | zenon_intro zenon_H103 ]. % 8.45/8.71 apply (zenon_L88_); trivial. % 8.45/8.71 apply (zenon_L89_); trivial. % 8.45/8.71 (* end of lemma zenon_L108_ *) % 8.45/8.71 assert (zenon_L109_ : ((op (e3) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H5a zenon_Hb3 zenon_H16d. % 8.45/8.71 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 8.45/8.71 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H16d. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H149. % 8.45/8.71 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 8.45/8.71 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H16e. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H5a. % 8.45/8.71 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H104]. % 8.45/8.71 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H14a. apply refl_equal. % 8.45/8.71 apply zenon_H104. apply sym_equal. exact zenon_Hb3. % 8.45/8.71 apply zenon_H14a. apply refl_equal. % 8.45/8.71 apply zenon_H14a. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L109_ *) % 8.45/8.71 assert (zenon_L110_ : (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H67 zenon_H29 zenon_Had. % 8.45/8.71 cut (((op (e1) (e2)) = (e1)) = ((e0) = (e1))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H67. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H29. % 8.45/8.71 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.71 cut (((op (e1) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H16f]. % 8.45/8.71 congruence. % 8.45/8.71 exact (zenon_H16f zenon_Had). % 8.45/8.71 apply zenon_H40. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L110_ *) % 8.45/8.71 assert (zenon_L111_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H170 zenon_H14e zenon_Hc3. % 8.45/8.71 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H170. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H14e. % 8.45/8.71 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H171]. % 8.45/8.71 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H172. apply refl_equal. % 8.45/8.71 apply zenon_H171. apply sym_equal. exact zenon_Hc3. % 8.45/8.71 (* end of lemma zenon_L111_ *) % 8.45/8.71 assert (zenon_L112_ : ((op (e2) (e2)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H3b zenon_Hc8 zenon_H173. % 8.45/8.71 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H3e ]. % 8.45/8.71 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e0)) = (op (e2) (e2)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H173. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H95. % 8.45/8.71 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 8.45/8.71 cut (((op (e2) (e2)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H174]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e2) (e0)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H174. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H3b. % 8.45/8.71 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 8.45/8.71 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H3e. apply refl_equal. % 8.45/8.71 apply zenon_H12d. apply sym_equal. exact zenon_Hc8. % 8.45/8.71 apply zenon_H3e. apply refl_equal. % 8.45/8.71 apply zenon_H3e. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L112_ *) % 8.45/8.71 assert (zenon_L113_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H175 zenon_H1d zenon_H1f. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H175). zenon_intro zenon_H1e. zenon_intro zenon_H176. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H176). zenon_intro zenon_H1e. zenon_intro zenon_H177. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H1e. zenon_intro zenon_H1e. % 8.45/8.71 apply (zenon_L1_); trivial. % 8.45/8.71 (* end of lemma zenon_L113_ *) % 8.45/8.71 assert (zenon_L114_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H178 zenon_H1f. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H178). zenon_intro zenon_H1e. zenon_intro zenon_H179. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H179). zenon_intro zenon_H1e. zenon_intro zenon_H17a. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_Hac. zenon_intro zenon_H1d. % 8.45/8.71 apply (zenon_L1_); trivial. % 8.45/8.71 (* end of lemma zenon_L114_ *) % 8.45/8.71 assert (zenon_L115_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H17b zenon_H25. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H17b). zenon_intro zenon_H1e. zenon_intro zenon_H17c. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H17c). zenon_intro zenon_H1e. zenon_intro zenon_H17d. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H143. zenon_intro zenon_H24. % 8.45/8.71 apply (zenon_L2_); trivial. % 8.45/8.71 (* end of lemma zenon_L115_ *) % 8.45/8.71 assert (zenon_L116_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H17b zenon_H25. % 8.45/8.71 apply (zenon_L115_); trivial. % 8.45/8.71 (* end of lemma zenon_L116_ *) % 8.45/8.71 assert (zenon_L117_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H17e zenon_H31. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H17e). zenon_intro zenon_H1e. zenon_intro zenon_H17f. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H17f). zenon_intro zenon_H1e. zenon_intro zenon_H180. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H14e. zenon_intro zenon_H30. % 8.45/8.71 apply (zenon_L4_); trivial. % 8.45/8.71 (* end of lemma zenon_L117_ *) % 8.45/8.71 assert (zenon_L118_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H17e zenon_H31. % 8.45/8.71 apply (zenon_L117_); trivial. % 8.45/8.71 (* end of lemma zenon_L118_ *) % 8.45/8.71 assert (zenon_L119_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H35 zenon_H73 zenon_Hb4. % 8.45/8.71 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H37 | zenon_intro zenon_H38 ]. % 8.45/8.71 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e0)) = (op (e1) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_Hb4. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H37. % 8.45/8.71 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 8.45/8.71 cut (((op (e1) (e3)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e1) (e0)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_Hb5. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H35. % 8.45/8.71 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 8.45/8.71 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H38. apply refl_equal. % 8.45/8.71 apply zenon_H76. apply sym_equal. exact zenon_H73. % 8.45/8.71 apply zenon_H38. apply refl_equal. % 8.45/8.71 apply zenon_H38. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L119_ *) % 8.45/8.71 assert (zenon_L120_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H181 zenon_H35 zenon_Hb4. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H1d. zenon_intro zenon_H182. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H182). zenon_intro zenon_Hac. zenon_intro zenon_H183. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H183). zenon_intro zenon_H6b. zenon_intro zenon_H73. % 8.45/8.71 apply (zenon_L119_); trivial. % 8.45/8.71 (* end of lemma zenon_L120_ *) % 8.45/8.71 assert (zenon_L121_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H184 zenon_H35 zenon_H36. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H184). zenon_intro zenon_H1d. zenon_intro zenon_H185. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H185). zenon_intro zenon_Hac. zenon_intro zenon_H186. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H186). zenon_intro zenon_H2a. zenon_intro zenon_H2a. % 8.45/8.71 apply (zenon_L5_); trivial. % 8.45/8.71 (* end of lemma zenon_L121_ *) % 8.45/8.71 assert (zenon_L122_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H187 zenon_H129 zenon_H35. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H187). zenon_intro zenon_H1d. zenon_intro zenon_H188. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H188). zenon_intro zenon_Hac. zenon_intro zenon_H189. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H15a. zenon_intro zenon_H29. % 8.45/8.71 apply (zenon_L74_); trivial. % 8.45/8.71 (* end of lemma zenon_L122_ *) % 8.45/8.71 assert (zenon_L123_ : (~((op (e0) (op (e0) (e3))) = (e3))) -> ((op (e0) (e3)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H18a zenon_H103. % 8.45/8.71 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (op (e0) (e3))) = (e3))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H18a. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H103. % 8.45/8.71 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.45/8.71 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H18b]. % 8.45/8.71 congruence. % 8.45/8.71 elim (classic ((op (e0) (op (e0) (e3))) = (op (e0) (op (e0) (e3))))); [ zenon_intro zenon_H18c | zenon_intro zenon_H18d ]. % 8.45/8.71 cut (((op (e0) (op (e0) (e3))) = (op (e0) (op (e0) (e3)))) = ((op (e0) (e3)) = (op (e0) (op (e0) (e3))))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H18b. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H18c. % 8.45/8.71 cut (((op (e0) (op (e0) (e3))) = (op (e0) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H18d]. % 8.45/8.71 cut (((op (e0) (op (e0) (e3))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H18e]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 8.45/8.71 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H3f. apply refl_equal. % 8.45/8.71 exact (zenon_H18f zenon_H103). % 8.45/8.71 apply zenon_H18d. apply refl_equal. % 8.45/8.71 apply zenon_H18d. apply refl_equal. % 8.45/8.71 apply zenon_H58. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L123_ *) % 8.45/8.71 assert (zenon_L124_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H35 zenon_Hb3 zenon_Ha3. % 8.45/8.71 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H58 ]. % 8.45/8.71 cut (((e3) = (e3)) = ((e1) = (e3))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_Ha3. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Ha4. % 8.45/8.71 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.45/8.71 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e1) (e3)) = (e1)) = ((e3) = (e1))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_Ha5. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H35. % 8.45/8.71 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.71 cut (((op (e1) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 8.45/8.71 congruence. % 8.45/8.71 exact (zenon_H190 zenon_Hb3). % 8.45/8.71 apply zenon_H40. apply refl_equal. % 8.45/8.71 apply zenon_H58. apply refl_equal. % 8.45/8.71 apply zenon_H58. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L124_ *) % 8.45/8.71 assert (zenon_L125_ : ((op (e2) (e1)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H191 zenon_Hc8 zenon_H192. % 8.45/8.71 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H193 | zenon_intro zenon_H16a ]. % 8.45/8.71 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (e0)) = (op (e2) (e1)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H192. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H193. % 8.45/8.71 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 8.45/8.71 cut (((op (e2) (e1)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H194]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e2) (e0)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H194. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H191. % 8.45/8.71 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 8.45/8.71 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H16a. apply refl_equal. % 8.45/8.71 apply zenon_H12d. apply sym_equal. exact zenon_Hc8. % 8.45/8.71 apply zenon_H16a. apply refl_equal. % 8.45/8.71 apply zenon_H16a. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L125_ *) % 8.45/8.71 assert (zenon_L126_ : ((op (e2) (e3)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H195 zenon_H196 zenon_H197. % 8.45/8.71 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H100 | zenon_intro zenon_Hea ]. % 8.45/8.71 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e1)) = (op (e2) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H197. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H100. % 8.45/8.71 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 8.45/8.71 cut (((op (e2) (e3)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H198]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e2) (e3)) = (e3)) = ((op (e2) (e3)) = (op (e2) (e1)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H198. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H195. % 8.45/8.71 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 8.45/8.71 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_Hea. apply refl_equal. % 8.45/8.71 apply zenon_H199. apply sym_equal. exact zenon_H196. % 8.45/8.71 apply zenon_Hea. apply refl_equal. % 8.45/8.71 apply zenon_Hea. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L126_ *) % 8.45/8.71 assert (zenon_L127_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H19a zenon_H1d zenon_H164 zenon_Hf4 zenon_H169 zenon_H192 zenon_Hc8 zenon_H195 zenon_H197. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H165 | zenon_intro zenon_H19b ]. % 8.45/8.71 apply (zenon_L101_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H15a | zenon_intro zenon_H19c ]. % 8.45/8.71 apply (zenon_L103_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H191 | zenon_intro zenon_H196 ]. % 8.45/8.71 apply (zenon_L125_); trivial. % 8.45/8.71 apply (zenon_L126_); trivial. % 8.45/8.71 (* end of lemma zenon_L127_ *) % 8.45/8.71 assert (zenon_L128_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H24 zenon_H7e zenon_H78. % 8.45/8.71 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H79 | zenon_intro zenon_H4b ]. % 8.45/8.71 cut (((e2) = (e2)) = ((e0) = (e2))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H78. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H79. % 8.45/8.71 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.71 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e0) (e2)) = (e0)) = ((e2) = (e0))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H7a. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H24. % 8.45/8.71 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.45/8.71 cut (((op (e0) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H11d]. % 8.45/8.71 congruence. % 8.45/8.71 exact (zenon_H11d zenon_H7e). % 8.45/8.71 apply zenon_H3f. apply refl_equal. % 8.45/8.71 apply zenon_H4b. apply refl_equal. % 8.45/8.71 apply zenon_H4b. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L128_ *) % 8.45/8.71 assert (zenon_L129_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((e0) = (e2))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H19d zenon_H78. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H19d). zenon_intro zenon_H24. zenon_intro zenon_H19e. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H19e). zenon_intro zenon_H143. zenon_intro zenon_H19f. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H19f). zenon_intro zenon_H7e. zenon_intro zenon_Hc8. % 8.45/8.71 apply (zenon_L128_); trivial. % 8.45/8.71 (* end of lemma zenon_L129_ *) % 8.45/8.71 assert (zenon_L130_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1a0 zenon_Hc8 zenon_H192. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a0). zenon_intro zenon_H24. zenon_intro zenon_H1a1. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a1). zenon_intro zenon_H143. zenon_intro zenon_H1a2. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a2). zenon_intro zenon_H93. zenon_intro zenon_H191. % 8.45/8.71 apply (zenon_L125_); trivial. % 8.45/8.71 (* end of lemma zenon_L130_ *) % 8.45/8.71 assert (zenon_L131_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1a3 zenon_Hc8 zenon_H173. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a3). zenon_intro zenon_H24. zenon_intro zenon_H1a4. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a4). zenon_intro zenon_H143. zenon_intro zenon_H1a5. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a5). zenon_intro zenon_H3b. zenon_intro zenon_H3b. % 8.45/8.71 apply (zenon_L112_); trivial. % 8.45/8.71 (* end of lemma zenon_L131_ *) % 8.45/8.71 assert (zenon_L132_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1a6 zenon_Hc8 zenon_H12b. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a6). zenon_intro zenon_H24. zenon_intro zenon_H1a7. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H143. zenon_intro zenon_H1a8. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hbd. zenon_intro zenon_H3c. % 8.45/8.71 apply (zenon_L75_); trivial. % 8.45/8.71 (* end of lemma zenon_L132_ *) % 8.45/8.71 assert (zenon_L133_ : (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e0)) -> False). % 8.45/8.71 do 0 intro. intros zenon_Hc2 zenon_H1a9 zenon_H14e. % 8.45/8.71 cut (((op (e3) (e0)) = (e3)) = ((e0) = (e3))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_Hc2. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H1a9. % 8.45/8.71 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.45/8.71 cut (((op (e3) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 8.45/8.71 congruence. % 8.45/8.71 exact (zenon_H1aa zenon_H14e). % 8.45/8.71 apply zenon_H58. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L133_ *) % 8.45/8.71 assert (zenon_L134_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1ab zenon_Hc2. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ab). zenon_intro zenon_H30. zenon_intro zenon_H1ac. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ac). zenon_intro zenon_H14e. zenon_intro zenon_H1ad. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H103. zenon_intro zenon_H1a9. % 8.45/8.71 apply (zenon_L133_); trivial. % 8.45/8.71 (* end of lemma zenon_L134_ *) % 8.45/8.71 assert (zenon_L135_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1ab zenon_Hc2. % 8.45/8.71 apply (zenon_L134_); trivial. % 8.45/8.71 (* end of lemma zenon_L135_ *) % 8.45/8.71 assert (zenon_L136_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1ae zenon_H35 zenon_Ha3. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_H30. zenon_intro zenon_H1af. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_H14e. zenon_intro zenon_H1b0. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb3. zenon_intro zenon_H1b1. % 8.45/8.71 apply (zenon_L124_); trivial. % 8.45/8.71 (* end of lemma zenon_L136_ *) % 8.45/8.71 assert (zenon_L137_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1b2 zenon_H127 zenon_H1d. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_H30. zenon_intro zenon_H1b3. % 8.45/8.71 apply (zenon_L73_); trivial. % 8.45/8.71 (* end of lemma zenon_L137_ *) % 8.45/8.71 assert (zenon_L138_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1b4 zenon_Heb zenon_H98. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b4). zenon_intro zenon_H30. zenon_intro zenon_H1b5. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b5). zenon_intro zenon_H14e. zenon_intro zenon_H1b6. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_H5a. zenon_intro zenon_H5a. % 8.45/8.71 apply (zenon_L53_); trivial. % 8.45/8.71 (* end of lemma zenon_L138_ *) % 8.45/8.71 assert (zenon_L139_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1b7 zenon_H1d zenon_H1f. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_H73. zenon_intro zenon_H1b8. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b8). zenon_intro zenon_H6b. zenon_intro zenon_H177. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H1e. zenon_intro zenon_H1e. % 8.45/8.71 apply (zenon_L1_); trivial. % 8.45/8.71 (* end of lemma zenon_L139_ *) % 8.45/8.71 assert (zenon_L140_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((e0) = (e1))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1b9 zenon_H67. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b9). zenon_intro zenon_H73. zenon_intro zenon_H1ba. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ba). zenon_intro zenon_H6b. zenon_intro zenon_H17a. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_Hac. zenon_intro zenon_H1d. % 8.45/8.71 apply (zenon_L77_); trivial. % 8.45/8.71 (* end of lemma zenon_L140_ *) % 8.45/8.71 assert (zenon_L141_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1bb zenon_H35 zenon_Hb4. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1bb). zenon_intro zenon_H73. zenon_intro zenon_H1bc. % 8.45/8.71 apply (zenon_L119_); trivial. % 8.45/8.71 (* end of lemma zenon_L141_ *) % 8.45/8.71 assert (zenon_L142_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1bd zenon_H127 zenon_H1d. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1bd). zenon_intro zenon_H73. zenon_intro zenon_H1be. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_H6b. zenon_intro zenon_H180. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H14e. zenon_intro zenon_H30. % 8.45/8.71 apply (zenon_L73_); trivial. % 8.45/8.71 (* end of lemma zenon_L142_ *) % 8.45/8.71 assert (zenon_L143_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1bf zenon_H35 zenon_Hb4. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1bf). zenon_intro zenon_H2a. zenon_intro zenon_H1c0. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c0). zenon_intro zenon_H2a. zenon_intro zenon_H183. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H183). zenon_intro zenon_H6b. zenon_intro zenon_H73. % 8.45/8.71 apply (zenon_L119_); trivial. % 8.45/8.71 (* end of lemma zenon_L143_ *) % 8.45/8.71 assert (zenon_L144_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1c1 zenon_H35 zenon_H36. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c1). zenon_intro zenon_H2a. zenon_intro zenon_H1c2. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c2). zenon_intro zenon_H2a. zenon_intro zenon_H186. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H186). zenon_intro zenon_H2a. zenon_intro zenon_H2a. % 8.45/8.71 apply (zenon_L5_); trivial. % 8.45/8.71 (* end of lemma zenon_L144_ *) % 8.45/8.71 assert (zenon_L145_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1c3 zenon_H2b. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c3). zenon_intro zenon_H2a. zenon_intro zenon_H1c4. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c4). zenon_intro zenon_H2a. zenon_intro zenon_H189. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H15a. zenon_intro zenon_H29. % 8.45/8.71 apply (zenon_L3_); trivial. % 8.45/8.71 (* end of lemma zenon_L145_ *) % 8.45/8.71 assert (zenon_L146_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1c3 zenon_H2b. % 8.45/8.71 apply (zenon_L145_); trivial. % 8.45/8.71 (* end of lemma zenon_L146_ *) % 8.45/8.71 assert (zenon_L147_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1c5 zenon_H36. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c5). zenon_intro zenon_H2a. zenon_intro zenon_H1c6. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c6). zenon_intro zenon_H2a. zenon_intro zenon_H1c7. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_Hf4. zenon_intro zenon_H35. % 8.45/8.71 apply (zenon_L5_); trivial. % 8.45/8.71 (* end of lemma zenon_L147_ *) % 8.45/8.71 assert (zenon_L148_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((op (e0) (op (e0) (e2))) = (e2))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1c8 zenon_H118. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_H29. zenon_intro zenon_H1c9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c9). zenon_intro zenon_H15a. zenon_intro zenon_H19f. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H19f). zenon_intro zenon_H7e. zenon_intro zenon_Hc8. % 8.45/8.71 apply (zenon_L70_); trivial. % 8.45/8.71 (* end of lemma zenon_L148_ *) % 8.45/8.71 assert (zenon_L149_ : (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H7d zenon_H191 zenon_H15a. % 8.45/8.71 cut (((op (e2) (e1)) = (e2)) = ((e1) = (e2))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H7d. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H191. % 8.45/8.71 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.71 cut (((op (e2) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H15f]. % 8.45/8.71 congruence. % 8.45/8.71 exact (zenon_H15f zenon_H15a). % 8.45/8.71 apply zenon_H4b. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L149_ *) % 8.45/8.71 assert (zenon_L150_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((e1) = (e2))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1ca zenon_H7d. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ca). zenon_intro zenon_H29. zenon_intro zenon_H1cb. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1cb). zenon_intro zenon_H15a. zenon_intro zenon_H1a2. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a2). zenon_intro zenon_H93. zenon_intro zenon_H191. % 8.45/8.71 apply (zenon_L149_); trivial. % 8.45/8.71 (* end of lemma zenon_L150_ *) % 8.45/8.71 assert (zenon_L151_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((e1) = (e2))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1ca zenon_H7d. % 8.45/8.71 apply (zenon_L150_); trivial. % 8.45/8.71 (* end of lemma zenon_L151_ *) % 8.45/8.71 assert (zenon_L152_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1cc zenon_Hc8 zenon_H173. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1cc). zenon_intro zenon_H29. zenon_intro zenon_H1cd. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1cd). zenon_intro zenon_H15a. zenon_intro zenon_H1a5. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a5). zenon_intro zenon_H3b. zenon_intro zenon_H3b. % 8.45/8.71 apply (zenon_L112_); trivial. % 8.45/8.71 (* end of lemma zenon_L152_ *) % 8.45/8.71 assert (zenon_L153_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1ce zenon_Hc8 zenon_H12b. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H29. zenon_intro zenon_H1cf. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_H15a. zenon_intro zenon_H1a8. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hbd. zenon_intro zenon_H3c. % 8.45/8.71 apply (zenon_L75_); trivial. % 8.45/8.71 (* end of lemma zenon_L153_ *) % 8.45/8.71 assert (zenon_L154_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H17e zenon_Hc2 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H17e). zenon_intro zenon_H1e. zenon_intro zenon_H17f. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H17f). zenon_intro zenon_H1e. zenon_intro zenon_H180. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H14e. zenon_intro zenon_H30. % 8.45/8.71 apply (zenon_L133_); trivial. % 8.45/8.71 (* end of lemma zenon_L154_ *) % 8.45/8.71 assert (zenon_L155_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H181 zenon_H29 zenon_Hab. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H1d. zenon_intro zenon_H182. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H182). zenon_intro zenon_Hac. zenon_intro zenon_H183. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H183). zenon_intro zenon_H6b. zenon_intro zenon_H73. % 8.45/8.71 apply (zenon_L93_); trivial. % 8.45/8.71 (* end of lemma zenon_L155_ *) % 8.45/8.71 assert (zenon_L156_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H184 zenon_H29 zenon_H2b. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H184). zenon_intro zenon_H1d. zenon_intro zenon_H185. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H185). zenon_intro zenon_Hac. zenon_intro zenon_H186. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H186). zenon_intro zenon_H2a. zenon_intro zenon_H2a. % 8.45/8.71 apply (zenon_L3_); trivial. % 8.45/8.71 (* end of lemma zenon_L156_ *) % 8.45/8.71 assert (zenon_L157_ : ((op (e2) (e1)) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H15a zenon_Hc9 zenon_H192. % 8.45/8.71 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H193 | zenon_intro zenon_H16a ]. % 8.45/8.71 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (e0)) = (op (e2) (e1)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H192. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H193. % 8.45/8.71 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 8.45/8.71 cut (((op (e2) (e1)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H194]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e2) (e1)) = (e1)) = ((op (e2) (e1)) = (op (e2) (e0)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H194. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H15a. % 8.45/8.71 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1d0]. % 8.45/8.71 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H16a. apply refl_equal. % 8.45/8.71 apply zenon_H1d0. apply sym_equal. exact zenon_Hc9. % 8.45/8.71 apply zenon_H16a. apply refl_equal. % 8.45/8.71 apply zenon_H16a. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L157_ *) % 8.45/8.71 assert (zenon_L158_ : (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> False). % 8.45/8.71 do 0 intro. intros zenon_Ha3 zenon_H1a9 zenon_Hf0. % 8.45/8.71 cut (((op (e3) (e0)) = (e3)) = ((e1) = (e3))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_Ha3. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H1a9. % 8.45/8.71 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.45/8.71 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 8.45/8.71 congruence. % 8.45/8.71 exact (zenon_H14f zenon_Hf0). % 8.45/8.71 apply zenon_H58. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L158_ *) % 8.45/8.71 assert (zenon_L159_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1d1 zenon_H129 zenon_H29. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1d1). zenon_intro zenon_H1d. zenon_intro zenon_H1d2. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1d2). zenon_intro zenon_Hac. zenon_intro zenon_H1c7. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_Hf4. zenon_intro zenon_H35. % 8.45/8.71 apply (zenon_L74_); trivial. % 8.45/8.71 (* end of lemma zenon_L159_ *) % 8.45/8.71 assert (zenon_L160_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H19d zenon_H3c zenon_H12b. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H19d). zenon_intro zenon_H24. zenon_intro zenon_H19e. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H19e). zenon_intro zenon_H143. zenon_intro zenon_H19f. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H19f). zenon_intro zenon_H7e. zenon_intro zenon_Hc8. % 8.45/8.71 apply (zenon_L75_); trivial. % 8.45/8.71 (* end of lemma zenon_L160_ *) % 8.45/8.71 assert (zenon_L161_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H29 zenon_H93 zenon_H7d. % 8.45/8.71 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H79 | zenon_intro zenon_H4b ]. % 8.45/8.71 cut (((e2) = (e2)) = ((e1) = (e2))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H7d. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H79. % 8.45/8.71 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.45/8.71 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hce]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e1) (e2)) = (e1)) = ((e2) = (e1))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_Hce. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H29. % 8.45/8.71 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.45/8.71 cut (((op (e1) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 8.45/8.71 congruence. % 8.45/8.71 exact (zenon_H159 zenon_H93). % 8.45/8.71 apply zenon_H40. apply refl_equal. % 8.45/8.71 apply zenon_H4b. apply refl_equal. % 8.45/8.71 apply zenon_H4b. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L161_ *) % 8.45/8.71 assert (zenon_L162_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1a0 zenon_H29 zenon_H7d. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a0). zenon_intro zenon_H24. zenon_intro zenon_H1a1. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a1). zenon_intro zenon_H143. zenon_intro zenon_H1a2. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a2). zenon_intro zenon_H93. zenon_intro zenon_H191. % 8.45/8.71 apply (zenon_L161_); trivial. % 8.45/8.71 (* end of lemma zenon_L162_ *) % 8.45/8.71 assert (zenon_L163_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1a3 zenon_H3a zenon_H3c. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a3). zenon_intro zenon_H24. zenon_intro zenon_H1a4. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a4). zenon_intro zenon_H143. zenon_intro zenon_H1a5. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a5). zenon_intro zenon_H3b. zenon_intro zenon_H3b. % 8.45/8.71 apply (zenon_L6_); trivial. % 8.45/8.71 (* end of lemma zenon_L163_ *) % 8.45/8.71 assert (zenon_L164_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1a6 zenon_H1d zenon_H124. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a6). zenon_intro zenon_H24. zenon_intro zenon_H1a7. % 8.45/8.71 apply (zenon_L72_); trivial. % 8.45/8.71 (* end of lemma zenon_L164_ *) % 8.45/8.71 assert (zenon_L165_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1d3 zenon_H1a9 zenon_H1b1. % 8.45/8.71 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H1d3. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H1a9. % 8.45/8.71 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1d4]. % 8.45/8.71 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H172. apply refl_equal. % 8.45/8.71 apply zenon_H1d4. apply sym_equal. exact zenon_H1b1. % 8.45/8.71 (* end of lemma zenon_L165_ *) % 8.45/8.71 assert (zenon_L166_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1ae zenon_H1d3 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_H30. zenon_intro zenon_H1af. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_H14e. zenon_intro zenon_H1b0. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb3. zenon_intro zenon_H1b1. % 8.45/8.71 apply (zenon_L165_); trivial. % 8.45/8.71 (* end of lemma zenon_L166_ *) % 8.45/8.71 assert (zenon_L167_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H170 zenon_H1a9 zenon_H98. % 8.45/8.71 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H170. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H1a9. % 8.45/8.71 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1d5]. % 8.45/8.71 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H172. apply refl_equal. % 8.45/8.71 apply zenon_H1d5. apply sym_equal. exact zenon_H98. % 8.45/8.71 (* end of lemma zenon_L167_ *) % 8.45/8.71 assert (zenon_L168_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1b2 zenon_H170 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_H30. zenon_intro zenon_H1b3. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b3). zenon_intro zenon_H14e. zenon_intro zenon_H1d6. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H195. zenon_intro zenon_H98. % 8.45/8.71 apply (zenon_L167_); trivial. % 8.45/8.71 (* end of lemma zenon_L168_ *) % 8.45/8.71 assert (zenon_L169_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1d7 zenon_H1a9 zenon_H5a. % 8.45/8.71 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H1d7. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H1a9. % 8.45/8.71 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 8.45/8.71 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H172. apply refl_equal. % 8.45/8.71 apply zenon_Hec. apply sym_equal. exact zenon_H5a. % 8.45/8.71 (* end of lemma zenon_L169_ *) % 8.45/8.71 assert (zenon_L170_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1b4 zenon_H1d7 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b4). zenon_intro zenon_H30. zenon_intro zenon_H1b5. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b5). zenon_intro zenon_H14e. zenon_intro zenon_H1b6. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_H5a. zenon_intro zenon_H5a. % 8.45/8.71 apply (zenon_L169_); trivial. % 8.45/8.71 (* end of lemma zenon_L170_ *) % 8.45/8.71 assert (zenon_L171_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1b7 zenon_H29 zenon_Hab. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_H73. zenon_intro zenon_H1b8. % 8.45/8.71 apply (zenon_L93_); trivial. % 8.45/8.71 (* end of lemma zenon_L171_ *) % 8.45/8.71 assert (zenon_L172_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1b9 zenon_H29 zenon_Hab. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b9). zenon_intro zenon_H73. zenon_intro zenon_H1ba. % 8.45/8.71 apply (zenon_L93_); trivial. % 8.45/8.71 (* end of lemma zenon_L172_ *) % 8.45/8.71 assert (zenon_L173_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1bb zenon_H29 zenon_Hab. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1bb). zenon_intro zenon_H73. zenon_intro zenon_H1bc. % 8.45/8.71 apply (zenon_L93_); trivial. % 8.45/8.71 (* end of lemma zenon_L173_ *) % 8.45/8.71 assert (zenon_L174_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1bd zenon_Hc2 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1bd). zenon_intro zenon_H73. zenon_intro zenon_H1be. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_H6b. zenon_intro zenon_H180. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H14e. zenon_intro zenon_H30. % 8.45/8.71 apply (zenon_L133_); trivial. % 8.45/8.71 (* end of lemma zenon_L174_ *) % 8.45/8.71 assert (zenon_L175_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1bf zenon_H29 zenon_H2b. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1bf). zenon_intro zenon_H2a. zenon_intro zenon_H1c0. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c0). zenon_intro zenon_H2a. zenon_intro zenon_H183. % 8.45/8.71 apply (zenon_L3_); trivial. % 8.45/8.71 (* end of lemma zenon_L175_ *) % 8.45/8.71 assert (zenon_L176_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1c1 zenon_H29 zenon_H2b. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c1). zenon_intro zenon_H2a. zenon_intro zenon_H1c2. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c2). zenon_intro zenon_H2a. zenon_intro zenon_H186. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H186). zenon_intro zenon_H2a. zenon_intro zenon_H2a. % 8.45/8.71 apply (zenon_L3_); trivial. % 8.45/8.71 (* end of lemma zenon_L176_ *) % 8.45/8.71 assert (zenon_L177_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1c5 zenon_H129 zenon_H29. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c5). zenon_intro zenon_H2a. zenon_intro zenon_H1c6. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c6). zenon_intro zenon_H2a. zenon_intro zenon_H1c7. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_Hf4. zenon_intro zenon_H35. % 8.45/8.71 apply (zenon_L74_); trivial. % 8.45/8.71 (* end of lemma zenon_L177_ *) % 8.45/8.71 assert (zenon_L178_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1c8 zenon_H3c zenon_H12b. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_H29. zenon_intro zenon_H1c9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c9). zenon_intro zenon_H15a. zenon_intro zenon_H19f. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H19f). zenon_intro zenon_H7e. zenon_intro zenon_Hc8. % 8.45/8.71 apply (zenon_L75_); trivial. % 8.45/8.71 (* end of lemma zenon_L178_ *) % 8.45/8.71 assert (zenon_L179_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1cc zenon_H3a zenon_H3c. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1cc). zenon_intro zenon_H29. zenon_intro zenon_H1cd. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1cd). zenon_intro zenon_H15a. zenon_intro zenon_H1a5. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a5). zenon_intro zenon_H3b. zenon_intro zenon_H3b. % 8.45/8.71 apply (zenon_L6_); trivial. % 8.45/8.71 (* end of lemma zenon_L179_ *) % 8.45/8.71 assert (zenon_L180_ : ((op (e3) (e2)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_Hbd zenon_H1d8 zenon_H1d9. % 8.45/8.71 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H9b | zenon_intro zenon_H9c ]. % 8.45/8.71 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (e1)) = (op (e3) (e2)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H1d9. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H9b. % 8.45/8.71 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 8.45/8.71 cut (((op (e3) (e2)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e3) (e2)) = (e2)) = ((op (e3) (e2)) = (op (e3) (e1)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H1da. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Hbd. % 8.45/8.71 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 8.45/8.71 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H9c. apply refl_equal. % 8.45/8.71 apply zenon_H1db. apply sym_equal. exact zenon_H1d8. % 8.45/8.71 apply zenon_H9c. apply refl_equal. % 8.45/8.71 apply zenon_H9c. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L180_ *) % 8.45/8.71 assert (zenon_L181_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1dc zenon_H1d zenon_H1dd zenon_H15a zenon_H169 zenon_H1d9 zenon_Hbd zenon_H1d3 zenon_H1a9. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H1df | zenon_intro zenon_H1de ]. % 8.45/8.71 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H1dd. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H1d. % 8.45/8.71 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1e0]. % 8.45/8.71 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H21. apply refl_equal. % 8.45/8.71 apply zenon_H1e0. apply sym_equal. exact zenon_H1df. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H1e1 ]. % 8.45/8.71 apply (zenon_L103_); trivial. % 8.45/8.71 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H1b1 ]. % 8.45/8.71 apply (zenon_L180_); trivial. % 8.45/8.71 apply (zenon_L165_); trivial. % 8.45/8.71 (* end of lemma zenon_L181_ *) % 8.45/8.71 assert (zenon_L182_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1e2 zenon_H129 zenon_H29. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1e2). zenon_intro zenon_H35. zenon_intro zenon_H1e3. % 8.45/8.71 apply (zenon_L74_); trivial. % 8.45/8.71 (* end of lemma zenon_L182_ *) % 8.45/8.71 assert (zenon_L183_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1e4 zenon_H1d3 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1e4). zenon_intro zenon_H35. zenon_intro zenon_H1e5. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1e5). zenon_intro zenon_Hf4. zenon_intro zenon_H1b0. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb3. zenon_intro zenon_H1b1. % 8.45/8.71 apply (zenon_L165_); trivial. % 8.45/8.71 (* end of lemma zenon_L183_ *) % 8.45/8.71 assert (zenon_L184_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1e6 zenon_H170 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H35. zenon_intro zenon_H1e7. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_Hf4. zenon_intro zenon_H1d6. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H195. zenon_intro zenon_H98. % 8.45/8.71 apply (zenon_L167_); trivial. % 8.45/8.71 (* end of lemma zenon_L184_ *) % 8.45/8.71 assert (zenon_L185_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1e8 zenon_H1d7 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1e8). zenon_intro zenon_H35. zenon_intro zenon_H1e9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1e9). zenon_intro zenon_Hf4. zenon_intro zenon_H1b6. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_H5a. zenon_intro zenon_H5a. % 8.45/8.71 apply (zenon_L169_); trivial. % 8.45/8.71 (* end of lemma zenon_L185_ *) % 8.45/8.71 assert (zenon_L186_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1ea zenon_H1d zenon_H1f. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ea). zenon_intro zenon_Hc8. zenon_intro zenon_H1eb. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1eb). zenon_intro zenon_H7e. zenon_intro zenon_H177. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H1e. zenon_intro zenon_H1e. % 8.45/8.71 apply (zenon_L1_); trivial. % 8.45/8.71 (* end of lemma zenon_L186_ *) % 8.45/8.71 assert (zenon_L187_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1ec zenon_H3c zenon_H12b. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_Hc8. zenon_intro zenon_H1ed. % 8.45/8.71 apply (zenon_L75_); trivial. % 8.45/8.71 (* end of lemma zenon_L187_ *) % 8.45/8.71 assert (zenon_L188_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((e0) = (e2))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1ee zenon_H78. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ee). zenon_intro zenon_Hc8. zenon_intro zenon_H1ef. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ef). zenon_intro zenon_H7e. zenon_intro zenon_H17d. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H143. zenon_intro zenon_H24. % 8.45/8.71 apply (zenon_L128_); trivial. % 8.45/8.71 (* end of lemma zenon_L188_ *) % 8.45/8.71 assert (zenon_L189_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1f0 zenon_Hc2 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_Hc8. zenon_intro zenon_H1f1. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1f1). zenon_intro zenon_H7e. zenon_intro zenon_H180. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H14e. zenon_intro zenon_H30. % 8.45/8.71 apply (zenon_L133_); trivial. % 8.45/8.71 (* end of lemma zenon_L189_ *) % 8.45/8.71 assert (zenon_L190_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1f2 zenon_H29 zenon_H7d. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1f2). zenon_intro zenon_H191. zenon_intro zenon_H1f3. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H93. zenon_intro zenon_H183. % 8.45/8.71 apply (zenon_L161_); trivial. % 8.45/8.71 (* end of lemma zenon_L190_ *) % 8.45/8.71 assert (zenon_L191_ : (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H197 zenon_H191 zenon_H3c. % 8.45/8.71 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e2) (e3)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H197. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H191. % 8.45/8.71 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H3d]. % 8.45/8.71 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H16a. apply refl_equal. % 8.45/8.71 apply zenon_H3d. apply sym_equal. exact zenon_H3c. % 8.45/8.71 (* end of lemma zenon_L191_ *) % 8.45/8.71 assert (zenon_L192_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1f4 zenon_H197 zenon_H3c. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1f4). zenon_intro zenon_H191. zenon_intro zenon_H1f5. % 8.45/8.71 apply (zenon_L191_); trivial. % 8.45/8.71 (* end of lemma zenon_L192_ *) % 8.45/8.71 assert (zenon_L193_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H175 zenon_H30 zenon_H31. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H175). zenon_intro zenon_H1e. zenon_intro zenon_H176. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H176). zenon_intro zenon_H1e. zenon_intro zenon_H177. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H1e. zenon_intro zenon_H1e. % 8.45/8.71 apply (zenon_L4_); trivial. % 8.45/8.71 (* end of lemma zenon_L193_ *) % 8.45/8.71 assert (zenon_L194_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H178 zenon_H30 zenon_H31. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H178). zenon_intro zenon_H1e. zenon_intro zenon_H179. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H179). zenon_intro zenon_H1e. zenon_intro zenon_H17a. % 8.45/8.71 apply (zenon_L4_); trivial. % 8.45/8.71 (* end of lemma zenon_L194_ *) % 8.45/8.71 assert (zenon_L195_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H17b zenon_H30 zenon_H31. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H17b). zenon_intro zenon_H1e. zenon_intro zenon_H17c. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H17c). zenon_intro zenon_H1e. zenon_intro zenon_H17d. % 8.45/8.71 apply (zenon_L4_); trivial. % 8.45/8.71 (* end of lemma zenon_L195_ *) % 8.45/8.71 assert (zenon_L196_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H187 zenon_H7d zenon_H191. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H187). zenon_intro zenon_H1d. zenon_intro zenon_H188. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H188). zenon_intro zenon_Hac. zenon_intro zenon_H189. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H15a. zenon_intro zenon_H29. % 8.45/8.71 apply (zenon_L149_); trivial. % 8.45/8.71 (* end of lemma zenon_L196_ *) % 8.45/8.71 assert (zenon_L197_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H19d zenon_H191 zenon_H192. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H19d). zenon_intro zenon_H24. zenon_intro zenon_H19e. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H19e). zenon_intro zenon_H143. zenon_intro zenon_H19f. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H19f). zenon_intro zenon_H7e. zenon_intro zenon_Hc8. % 8.45/8.71 apply (zenon_L125_); trivial. % 8.45/8.71 (* end of lemma zenon_L197_ *) % 8.45/8.71 assert (zenon_L198_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e2)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1f6 zenon_H191 zenon_H3b. % 8.45/8.71 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e2) (e2)))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H1f6. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H191. % 8.45/8.71 cut (((e2) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f7]. % 8.45/8.71 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 8.45/8.71 congruence. % 8.45/8.71 apply zenon_H16a. apply refl_equal. % 8.45/8.71 apply zenon_H1f7. apply sym_equal. exact zenon_H3b. % 8.45/8.71 (* end of lemma zenon_L198_ *) % 8.45/8.71 assert (zenon_L199_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1a3 zenon_H1f6 zenon_H191. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a3). zenon_intro zenon_H24. zenon_intro zenon_H1a4. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a4). zenon_intro zenon_H143. zenon_intro zenon_H1a5. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a5). zenon_intro zenon_H3b. zenon_intro zenon_H3b. % 8.45/8.71 apply (zenon_L198_); trivial. % 8.45/8.71 (* end of lemma zenon_L199_ *) % 8.45/8.71 assert (zenon_L200_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1a6 zenon_H197 zenon_H191. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a6). zenon_intro zenon_H24. zenon_intro zenon_H1a7. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H143. zenon_intro zenon_H1a8. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hbd. zenon_intro zenon_H3c. % 8.45/8.71 apply (zenon_L191_); trivial. % 8.45/8.71 (* end of lemma zenon_L200_ *) % 8.45/8.71 assert (zenon_L201_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H30 zenon_H103 zenon_Hc2. % 8.45/8.71 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H58 ]. % 8.45/8.71 cut (((e3) = (e3)) = ((e0) = (e3))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_Hc2. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_Ha4. % 8.45/8.71 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.45/8.71 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 8.45/8.71 congruence. % 8.45/8.71 cut (((op (e0) (e3)) = (e0)) = ((e3) = (e0))). % 8.45/8.71 intro zenon_D_pnotp. % 8.45/8.71 apply zenon_H1f8. % 8.45/8.71 rewrite <- zenon_D_pnotp. % 8.45/8.71 exact zenon_H30. % 8.45/8.71 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.45/8.71 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 8.45/8.71 congruence. % 8.45/8.71 exact (zenon_H18f zenon_H103). % 8.45/8.71 apply zenon_H3f. apply refl_equal. % 8.45/8.71 apply zenon_H58. apply refl_equal. % 8.45/8.71 apply zenon_H58. apply refl_equal. % 8.45/8.71 (* end of lemma zenon_L201_ *) % 8.45/8.71 assert (zenon_L202_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1ab zenon_Hc2. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ab). zenon_intro zenon_H30. zenon_intro zenon_H1ac. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ac). zenon_intro zenon_H14e. zenon_intro zenon_H1ad. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H103. zenon_intro zenon_H1a9. % 8.45/8.71 apply (zenon_L201_); trivial. % 8.45/8.71 (* end of lemma zenon_L202_ *) % 8.45/8.71 assert (zenon_L203_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1c3 zenon_H7d zenon_H191. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c3). zenon_intro zenon_H2a. zenon_intro zenon_H1c4. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c4). zenon_intro zenon_H2a. zenon_intro zenon_H189. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H15a. zenon_intro zenon_H29. % 8.45/8.71 apply (zenon_L149_); trivial. % 8.45/8.71 (* end of lemma zenon_L203_ *) % 8.45/8.71 assert (zenon_L204_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1c8 zenon_H191 zenon_H192. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_H29. zenon_intro zenon_H1c9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c9). zenon_intro zenon_H15a. zenon_intro zenon_H19f. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H19f). zenon_intro zenon_H7e. zenon_intro zenon_Hc8. % 8.45/8.71 apply (zenon_L125_); trivial. % 8.45/8.71 (* end of lemma zenon_L204_ *) % 8.45/8.71 assert (zenon_L205_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((e1) = (e2))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1ca zenon_H7d. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ca). zenon_intro zenon_H29. zenon_intro zenon_H1cb. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1cb). zenon_intro zenon_H15a. zenon_intro zenon_H1a2. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a2). zenon_intro zenon_H93. zenon_intro zenon_H191. % 8.45/8.71 apply (zenon_L161_); trivial. % 8.45/8.71 (* end of lemma zenon_L205_ *) % 8.45/8.71 assert (zenon_L206_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1cc zenon_H1f6 zenon_H191. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1cc). zenon_intro zenon_H29. zenon_intro zenon_H1cd. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1cd). zenon_intro zenon_H15a. zenon_intro zenon_H1a5. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a5). zenon_intro zenon_H3b. zenon_intro zenon_H3b. % 8.45/8.71 apply (zenon_L198_); trivial. % 8.45/8.71 (* end of lemma zenon_L206_ *) % 8.45/8.71 assert (zenon_L207_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1ce zenon_H197 zenon_H191. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H29. zenon_intro zenon_H1cf. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_H15a. zenon_intro zenon_H1a8. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hbd. zenon_intro zenon_H3c. % 8.45/8.71 apply (zenon_L191_); trivial. % 8.45/8.71 (* end of lemma zenon_L207_ *) % 8.45/8.71 assert (zenon_L208_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1e2 zenon_H30 zenon_Hc2. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1e2). zenon_intro zenon_H35. zenon_intro zenon_H1e3. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1e3). zenon_intro zenon_Hf4. zenon_intro zenon_H1ad. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H103. zenon_intro zenon_H1a9. % 8.45/8.71 apply (zenon_L201_); trivial. % 8.45/8.71 (* end of lemma zenon_L208_ *) % 8.45/8.71 assert (zenon_L209_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1ea zenon_H191 zenon_H192. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ea). zenon_intro zenon_Hc8. zenon_intro zenon_H1eb. % 8.45/8.71 apply (zenon_L125_); trivial. % 8.45/8.71 (* end of lemma zenon_L209_ *) % 8.45/8.71 assert (zenon_L210_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1ec zenon_H191 zenon_H192. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_Hc8. zenon_intro zenon_H1ed. % 8.45/8.71 apply (zenon_L125_); trivial. % 8.45/8.71 (* end of lemma zenon_L210_ *) % 8.45/8.71 assert (zenon_L211_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1ee zenon_H191 zenon_H192. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ee). zenon_intro zenon_Hc8. zenon_intro zenon_H1ef. % 8.45/8.71 apply (zenon_L125_); trivial. % 8.45/8.71 (* end of lemma zenon_L211_ *) % 8.45/8.71 assert (zenon_L212_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1f4 zenon_H29 zenon_H7d. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1f4). zenon_intro zenon_H191. zenon_intro zenon_H1f5. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1f5). zenon_intro zenon_H93. zenon_intro zenon_H186. % 8.45/8.71 apply (zenon_L161_); trivial. % 8.45/8.71 (* end of lemma zenon_L212_ *) % 8.45/8.71 assert (zenon_L213_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((e1) = (e2))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1f9 zenon_H7d. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1f9). zenon_intro zenon_H191. zenon_intro zenon_H1fa. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1fa). zenon_intro zenon_H93. zenon_intro zenon_H189. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H15a. zenon_intro zenon_H29. % 8.45/8.71 apply (zenon_L149_); trivial. % 8.45/8.71 (* end of lemma zenon_L213_ *) % 8.45/8.71 assert (zenon_L214_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1fb zenon_H129 zenon_H29. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H191. zenon_intro zenon_H1fc. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_H93. zenon_intro zenon_H1c7. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_Hf4. zenon_intro zenon_H35. % 8.45/8.71 apply (zenon_L74_); trivial. % 8.45/8.71 (* end of lemma zenon_L214_ *) % 8.45/8.71 assert (zenon_L215_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1fd zenon_H191 zenon_H192. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1fd). zenon_intro zenon_H3b. zenon_intro zenon_H1fe. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1fe). zenon_intro zenon_H3b. zenon_intro zenon_H19f. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H19f). zenon_intro zenon_H7e. zenon_intro zenon_Hc8. % 8.45/8.71 apply (zenon_L125_); trivial. % 8.45/8.71 (* end of lemma zenon_L215_ *) % 8.45/8.71 assert (zenon_L216_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H1ff zenon_H1f6. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ff). zenon_intro zenon_H3b. zenon_intro zenon_H200. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H200). zenon_intro zenon_H3b. zenon_intro zenon_H1a2. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a2). zenon_intro zenon_H93. zenon_intro zenon_H191. % 8.45/8.71 apply (zenon_L198_); trivial. % 8.45/8.71 (* end of lemma zenon_L216_ *) % 8.45/8.71 assert (zenon_L217_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H201 zenon_H1f6 zenon_H191. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H201). zenon_intro zenon_H3b. zenon_intro zenon_H202. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H202). zenon_intro zenon_H3b. zenon_intro zenon_H1a5. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a5). zenon_intro zenon_H3b. zenon_intro zenon_H3b. % 8.45/8.71 apply (zenon_L198_); trivial. % 8.45/8.71 (* end of lemma zenon_L217_ *) % 8.45/8.71 assert (zenon_L218_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H203 zenon_H197 zenon_H191. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H203). zenon_intro zenon_H3b. zenon_intro zenon_H204. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H204). zenon_intro zenon_H3b. zenon_intro zenon_H1a8. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hbd. zenon_intro zenon_H3c. % 8.45/8.71 apply (zenon_L191_); trivial. % 8.45/8.71 (* end of lemma zenon_L218_ *) % 8.45/8.71 assert (zenon_L219_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H205 zenon_H30 zenon_Hc2. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H3c. zenon_intro zenon_H206. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_Hbd. zenon_intro zenon_H1ad. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H103. zenon_intro zenon_H1a9. % 8.45/8.71 apply (zenon_L201_); trivial. % 8.45/8.71 (* end of lemma zenon_L219_ *) % 8.45/8.71 assert (zenon_L220_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H207 zenon_H1d3 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H207). zenon_intro zenon_H3c. zenon_intro zenon_H208. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H208). zenon_intro zenon_Hbd. zenon_intro zenon_H1b0. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb3. zenon_intro zenon_H1b1. % 8.45/8.71 apply (zenon_L165_); trivial. % 8.45/8.71 (* end of lemma zenon_L220_ *) % 8.45/8.71 assert (zenon_L221_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H209 zenon_H170 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H209). zenon_intro zenon_H3c. zenon_intro zenon_H20a. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H20a). zenon_intro zenon_Hbd. zenon_intro zenon_H1d6. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H195. zenon_intro zenon_H98. % 8.45/8.71 apply (zenon_L167_); trivial. % 8.45/8.71 (* end of lemma zenon_L221_ *) % 8.45/8.71 assert (zenon_L222_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H20b zenon_H1d7 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H20b). zenon_intro zenon_H3c. zenon_intro zenon_H20c. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H20c). zenon_intro zenon_Hbd. zenon_intro zenon_H1b6. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_H5a. zenon_intro zenon_H5a. % 8.45/8.71 apply (zenon_L169_); trivial. % 8.45/8.71 (* end of lemma zenon_L222_ *) % 8.45/8.71 assert (zenon_L223_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H20d zenon_H30 zenon_Hc2. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H20d). zenon_intro zenon_H1a9. zenon_intro zenon_H20e. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H20e). zenon_intro zenon_H103. zenon_intro zenon_H177. % 8.45/8.71 apply (zenon_L201_); trivial. % 8.45/8.71 (* end of lemma zenon_L223_ *) % 8.45/8.71 assert (zenon_L224_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H20f zenon_H30 zenon_Hc2. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H20f). zenon_intro zenon_H1a9. zenon_intro zenon_H210. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H210). zenon_intro zenon_H103. zenon_intro zenon_H17a. % 8.45/8.71 apply (zenon_L201_); trivial. % 8.45/8.71 (* end of lemma zenon_L224_ *) % 8.45/8.71 assert (zenon_L225_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H211 zenon_H30 zenon_Hc2. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H211). zenon_intro zenon_H1a9. zenon_intro zenon_H212. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H212). zenon_intro zenon_H103. zenon_intro zenon_H17d. % 8.45/8.71 apply (zenon_L201_); trivial. % 8.45/8.71 (* end of lemma zenon_L225_ *) % 8.45/8.71 assert (zenon_L226_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((e0) = (e3))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H213 zenon_Hc2. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H213). zenon_intro zenon_H1a9. zenon_intro zenon_H214. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H214). zenon_intro zenon_H103. zenon_intro zenon_H180. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H14e. zenon_intro zenon_H30. % 8.45/8.71 apply (zenon_L133_); trivial. % 8.45/8.71 (* end of lemma zenon_L226_ *) % 8.45/8.71 assert (zenon_L227_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H215 zenon_H1d3 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H215). zenon_intro zenon_H1b1. zenon_intro zenon_H216. % 8.45/8.71 apply (zenon_L165_); trivial. % 8.45/8.71 (* end of lemma zenon_L227_ *) % 8.45/8.71 assert (zenon_L228_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H217 zenon_H1d3 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H217). zenon_intro zenon_H1b1. zenon_intro zenon_H218. % 8.45/8.71 apply (zenon_L165_); trivial. % 8.45/8.71 (* end of lemma zenon_L228_ *) % 8.45/8.71 assert (zenon_L229_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H219 zenon_H1d3 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H219). zenon_intro zenon_H1b1. zenon_intro zenon_H21a. % 8.45/8.71 apply (zenon_L165_); trivial. % 8.45/8.71 (* end of lemma zenon_L229_ *) % 8.45/8.71 assert (zenon_L230_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H21b zenon_H1d3 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H21b). zenon_intro zenon_H1b1. zenon_intro zenon_H21c. % 8.45/8.71 apply (zenon_L165_); trivial. % 8.45/8.71 (* end of lemma zenon_L230_ *) % 8.45/8.71 assert (zenon_L231_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H21d zenon_H170 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H98. zenon_intro zenon_H21e. % 8.45/8.71 apply (zenon_L167_); trivial. % 8.45/8.71 (* end of lemma zenon_L231_ *) % 8.45/8.71 assert (zenon_L232_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H21f zenon_H170 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H21f). zenon_intro zenon_H98. zenon_intro zenon_H220. % 8.45/8.71 apply (zenon_L167_); trivial. % 8.45/8.71 (* end of lemma zenon_L232_ *) % 8.45/8.71 assert (zenon_L233_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H221 zenon_H170 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H221). zenon_intro zenon_H98. zenon_intro zenon_H222. % 8.45/8.71 apply (zenon_L167_); trivial. % 8.45/8.71 (* end of lemma zenon_L233_ *) % 8.45/8.71 assert (zenon_L234_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H223 zenon_H170 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H98. zenon_intro zenon_H224. % 8.45/8.71 apply (zenon_L167_); trivial. % 8.45/8.71 (* end of lemma zenon_L234_ *) % 8.45/8.71 assert (zenon_L235_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 8.45/8.71 do 0 intro. intros zenon_H225 zenon_H1d7. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H225). zenon_intro zenon_H5a. zenon_intro zenon_H226. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H226). zenon_intro zenon_H5a. zenon_intro zenon_H1ad. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H103. zenon_intro zenon_H1a9. % 8.45/8.71 apply (zenon_L169_); trivial. % 8.45/8.71 (* end of lemma zenon_L235_ *) % 8.45/8.71 assert (zenon_L236_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H227 zenon_H1d3 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H227). zenon_intro zenon_H5a. zenon_intro zenon_H228. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H228). zenon_intro zenon_H5a. zenon_intro zenon_H1b0. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb3. zenon_intro zenon_H1b1. % 8.45/8.71 apply (zenon_L165_); trivial. % 8.45/8.71 (* end of lemma zenon_L236_ *) % 8.45/8.71 assert (zenon_L237_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.45/8.71 do 0 intro. intros zenon_H229 zenon_H170 zenon_H1a9. % 8.45/8.71 apply (zenon_and_s _ _ zenon_H229). zenon_intro zenon_H5a. zenon_intro zenon_H22a. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H22a). zenon_intro zenon_H5a. zenon_intro zenon_H1d6. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H195. zenon_intro zenon_H98. % 8.54/8.72 apply (zenon_L167_); trivial. % 8.54/8.72 (* end of lemma zenon_L237_ *) % 8.54/8.72 assert (zenon_L238_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H22b zenon_H1d7 zenon_H1a9. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H22b). zenon_intro zenon_H5a. zenon_intro zenon_H22c. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H22c). zenon_intro zenon_H5a. zenon_intro zenon_H1b6. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_H5a. zenon_intro zenon_H5a. % 8.54/8.72 apply (zenon_L169_); trivial. % 8.54/8.72 (* end of lemma zenon_L238_ *) % 8.54/8.72 assert (zenon_L239_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H22d zenon_H170 zenon_H1d3 zenon_Hc2 zenon_H1f6 zenon_H192 zenon_H7d zenon_H2b zenon_Hab zenon_H31 zenon_H22e zenon_H29 zenon_H129 zenon_H191 zenon_H197 zenon_H1d7 zenon_H1a9. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.72 apply (zenon_L193_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.72 apply (zenon_L194_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.72 apply (zenon_L195_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.72 apply (zenon_L154_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.72 apply (zenon_L155_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.72 apply (zenon_L156_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.72 apply (zenon_L196_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.72 apply (zenon_L159_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.72 apply (zenon_L197_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.72 apply (zenon_L162_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.72 apply (zenon_L199_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.72 apply (zenon_L200_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.72 apply (zenon_L202_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.72 apply (zenon_L166_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.72 apply (zenon_L168_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.72 apply (zenon_L170_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.72 apply (zenon_L171_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.72 apply (zenon_L172_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.72 apply (zenon_L173_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.72 apply (zenon_L174_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.72 apply (zenon_L175_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.72 apply (zenon_L176_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.72 apply (zenon_L203_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.72 apply (zenon_L177_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.72 apply (zenon_L204_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.72 apply (zenon_L205_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.72 apply (zenon_L206_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.72 apply (zenon_L207_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.72 apply (zenon_L208_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.72 apply (zenon_L183_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.72 apply (zenon_L184_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.72 apply (zenon_L185_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.72 apply (zenon_L209_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.72 apply (zenon_L210_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.72 apply (zenon_L211_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.72 apply (zenon_L189_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.72 apply (zenon_L190_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.72 apply (zenon_L212_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.72 apply (zenon_L213_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.72 apply (zenon_L214_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.72 apply (zenon_L215_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.72 apply (zenon_L216_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.72 apply (zenon_L217_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.72 apply (zenon_L218_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.72 apply (zenon_L219_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.72 apply (zenon_L220_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.72 apply (zenon_L221_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.72 apply (zenon_L222_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.72 apply (zenon_L223_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.72 apply (zenon_L224_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.72 apply (zenon_L225_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.72 apply (zenon_L226_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.72 apply (zenon_L227_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.72 apply (zenon_L228_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.72 apply (zenon_L229_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.72 apply (zenon_L230_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.72 apply (zenon_L231_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.72 apply (zenon_L232_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.72 apply (zenon_L233_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.72 apply (zenon_L234_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.72 apply (zenon_L235_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.72 apply (zenon_L236_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.72 apply (zenon_L237_); trivial. % 8.54/8.72 apply (zenon_L238_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.54/8.72 apply (zenon_L74_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.54/8.72 apply (zenon_L191_); trivial. % 8.54/8.72 apply (zenon_L169_); trivial. % 8.54/8.72 (* end of lemma zenon_L239_ *) % 8.54/8.72 assert (zenon_L240_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H1f9 zenon_H22d zenon_H170 zenon_H1d3 zenon_Hc2 zenon_H1f6 zenon_H192 zenon_H7d zenon_H2b zenon_Hab zenon_H31 zenon_H22e zenon_H129 zenon_H197 zenon_H1d7 zenon_H1a9. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1f9). zenon_intro zenon_H191. zenon_intro zenon_H1fa. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1fa). zenon_intro zenon_H93. zenon_intro zenon_H189. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H15a. zenon_intro zenon_H29. % 8.54/8.72 apply (zenon_L239_); trivial. % 8.54/8.72 (* end of lemma zenon_L240_ *) % 8.54/8.72 assert (zenon_L241_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H1fd zenon_H173. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1fd). zenon_intro zenon_H3b. zenon_intro zenon_H1fe. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1fe). zenon_intro zenon_H3b. zenon_intro zenon_H19f. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H19f). zenon_intro zenon_H7e. zenon_intro zenon_Hc8. % 8.54/8.72 apply (zenon_L112_); trivial. % 8.54/8.72 (* end of lemma zenon_L241_ *) % 8.54/8.72 assert (zenon_L242_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H1ff zenon_H1f6. % 8.54/8.72 apply (zenon_L216_); trivial. % 8.54/8.72 (* end of lemma zenon_L242_ *) % 8.54/8.72 assert (zenon_L243_ : ((op (e3) (e0)) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H1a9 zenon_H26f zenon_H270. % 8.54/8.72 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H271 | zenon_intro zenon_H172 ]. % 8.54/8.72 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e0) (e0)) = (op (e3) (e0)))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H270. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H271. % 8.54/8.72 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 8.54/8.72 cut (((op (e3) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H272]. % 8.54/8.72 congruence. % 8.54/8.72 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e0) (e0)))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H272. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H1a9. % 8.54/8.72 cut (((e3) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H273]. % 8.54/8.72 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 8.54/8.72 congruence. % 8.54/8.72 apply zenon_H172. apply refl_equal. % 8.54/8.72 apply zenon_H273. apply sym_equal. exact zenon_H26f. % 8.54/8.72 apply zenon_H172. apply refl_equal. % 8.54/8.72 apply zenon_H172. apply refl_equal. % 8.54/8.72 (* end of lemma zenon_L243_ *) % 8.54/8.72 assert (zenon_L244_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e3)) -> (~((e0) = (e3))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H1d zenon_H274 zenon_Hc2. % 8.54/8.72 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H58 ]. % 8.54/8.72 cut (((e3) = (e3)) = ((e0) = (e3))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_Hc2. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_Ha4. % 8.54/8.72 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.72 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 8.54/8.72 congruence. % 8.54/8.72 cut (((op (e0) (e1)) = (e0)) = ((e3) = (e0))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H1f8. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H1d. % 8.54/8.72 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.54/8.72 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H275]. % 8.54/8.72 congruence. % 8.54/8.72 exact (zenon_H275 zenon_H274). % 8.54/8.72 apply zenon_H3f. apply refl_equal. % 8.54/8.72 apply zenon_H58. apply refl_equal. % 8.54/8.72 apply zenon_H58. apply refl_equal. % 8.54/8.72 (* end of lemma zenon_L244_ *) % 8.54/8.72 assert (zenon_L245_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H71 zenon_H276 zenon_Ha3. % 8.54/8.72 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H58 ]. % 8.54/8.72 cut (((e3) = (e3)) = ((e1) = (e3))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_Ha3. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_Ha4. % 8.54/8.72 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.72 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 8.54/8.72 congruence. % 8.54/8.72 cut (((op (e0) (e2)) = (e1)) = ((e3) = (e1))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_Ha5. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H71. % 8.54/8.72 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.54/8.72 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H277]. % 8.54/8.72 congruence. % 8.54/8.72 exact (zenon_H277 zenon_H276). % 8.54/8.72 apply zenon_H40. apply refl_equal. % 8.54/8.72 apply zenon_H58. apply refl_equal. % 8.54/8.72 apply zenon_H58. apply refl_equal. % 8.54/8.72 (* end of lemma zenon_L245_ *) % 8.54/8.72 assert (zenon_L246_ : ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H35 zenon_Hd6 zenon_Hd0. % 8.54/8.72 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H37 | zenon_intro zenon_H38 ]. % 8.54/8.72 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e0) (e3)) = (op (e1) (e3)))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_Hd0. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H37. % 8.54/8.72 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 8.54/8.72 cut (((op (e1) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 8.54/8.72 congruence. % 8.54/8.72 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e0) (e3)))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H278. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H35. % 8.54/8.72 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 8.54/8.72 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 8.54/8.72 congruence. % 8.54/8.72 apply zenon_H38. apply refl_equal. % 8.54/8.72 apply zenon_H279. apply sym_equal. exact zenon_Hd6. % 8.54/8.72 apply zenon_H38. apply refl_equal. % 8.54/8.72 apply zenon_H38. apply refl_equal. % 8.54/8.72 (* end of lemma zenon_L246_ *) % 8.54/8.72 assert (zenon_L247_ : (~((op (e1) (op (e1) (e1))) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H41 zenon_H35 zenon_Ha2. % 8.54/8.72 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (op (e1) (e1))) = (e1))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H41. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H35. % 8.54/8.72 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.54/8.72 cut (((op (e1) (e3)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H27a]. % 8.54/8.72 congruence. % 8.54/8.72 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_H43 | zenon_intro zenon_H44 ]. % 8.54/8.72 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e3)) = (op (e1) (op (e1) (e1))))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H27a. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H43. % 8.54/8.72 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 8.54/8.72 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H27b]. % 8.54/8.72 congruence. % 8.54/8.72 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 8.54/8.72 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.54/8.72 congruence. % 8.54/8.72 apply zenon_H40. apply refl_equal. % 8.54/8.72 exact (zenon_Ha6 zenon_Ha2). % 8.54/8.72 apply zenon_H44. apply refl_equal. % 8.54/8.72 apply zenon_H44. apply refl_equal. % 8.54/8.72 apply zenon_H40. apply refl_equal. % 8.54/8.72 (* end of lemma zenon_L247_ *) % 8.54/8.72 assert (zenon_L248_ : ((op (e2) (e0)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H143 zenon_Hac zenon_H145. % 8.54/8.72 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 8.54/8.72 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e1) (e0)) = (op (e2) (e0)))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H145. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H138. % 8.54/8.72 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 8.54/8.72 cut (((op (e2) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 8.54/8.72 congruence. % 8.54/8.72 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e1) (e0)))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H146. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H143. % 8.54/8.72 cut (((e0) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H27c]. % 8.54/8.72 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 8.54/8.72 congruence. % 8.54/8.72 apply zenon_H139. apply refl_equal. % 8.54/8.72 apply zenon_H27c. apply sym_equal. exact zenon_Hac. % 8.54/8.72 apply zenon_H139. apply refl_equal. % 8.54/8.72 apply zenon_H139. apply refl_equal. % 8.54/8.72 (* end of lemma zenon_L248_ *) % 8.54/8.72 assert (zenon_L249_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H192 zenon_H143 zenon_H165. % 8.54/8.72 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H192. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H143. % 8.54/8.72 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H166]. % 8.54/8.72 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 8.54/8.72 congruence. % 8.54/8.72 apply zenon_H139. apply refl_equal. % 8.54/8.72 apply zenon_H166. apply sym_equal. exact zenon_H165. % 8.54/8.72 (* end of lemma zenon_L249_ *) % 8.54/8.72 assert (zenon_L250_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e0)) = (e1)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H137 zenon_H66 zenon_Hc9. % 8.54/8.72 cut (((op (e0) (e0)) = (e1)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H137. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H66. % 8.54/8.72 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1d0]. % 8.54/8.72 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H27d]. % 8.54/8.72 congruence. % 8.54/8.72 apply zenon_H27d. apply refl_equal. % 8.54/8.72 apply zenon_H1d0. apply sym_equal. exact zenon_Hc9. % 8.54/8.72 (* end of lemma zenon_L250_ *) % 8.54/8.72 assert (zenon_L251_ : ((op (e3) (e0)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H1a9 zenon_H27e zenon_H27f. % 8.54/8.72 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H271 | zenon_intro zenon_H172 ]. % 8.54/8.72 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e2) (e0)) = (op (e3) (e0)))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H27f. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H271. % 8.54/8.72 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 8.54/8.72 cut (((op (e3) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H280]. % 8.54/8.72 congruence. % 8.54/8.72 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e2) (e0)))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H280. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H1a9. % 8.54/8.72 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H281]. % 8.54/8.72 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 8.54/8.72 congruence. % 8.54/8.72 apply zenon_H172. apply refl_equal. % 8.54/8.72 apply zenon_H281. apply sym_equal. exact zenon_H27e. % 8.54/8.72 apply zenon_H172. apply refl_equal. % 8.54/8.72 apply zenon_H172. apply refl_equal. % 8.54/8.72 (* end of lemma zenon_L251_ *) % 8.54/8.72 assert (zenon_L252_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H282 zenon_H165 zenon_H192 zenon_H66 zenon_H137 zenon_H173 zenon_H3b zenon_H1a9 zenon_H27f. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H143 | zenon_intro zenon_H283 ]. % 8.54/8.72 apply (zenon_L249_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H284 ]. % 8.54/8.72 apply (zenon_L250_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H27e ]. % 8.54/8.72 apply (zenon_L112_); trivial. % 8.54/8.72 apply (zenon_L251_); trivial. % 8.54/8.72 (* end of lemma zenon_L252_ *) % 8.54/8.72 assert (zenon_L253_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H12b zenon_H143 zenon_H10f. % 8.54/8.72 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e2) (e3)))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H12b. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H143. % 8.54/8.72 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 8.54/8.72 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 8.54/8.72 congruence. % 8.54/8.72 apply zenon_H139. apply refl_equal. % 8.54/8.72 apply zenon_H14d. apply sym_equal. exact zenon_H10f. % 8.54/8.72 (* end of lemma zenon_L253_ *) % 8.54/8.72 assert (zenon_L254_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H282 zenon_H10f zenon_H12b zenon_H66 zenon_H137 zenon_H173 zenon_H3b zenon_H1a9 zenon_H27f. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H143 | zenon_intro zenon_H283 ]. % 8.54/8.72 apply (zenon_L253_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H284 ]. % 8.54/8.72 apply (zenon_L250_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H27e ]. % 8.54/8.72 apply (zenon_L112_); trivial. % 8.54/8.72 apply (zenon_L251_); trivial. % 8.54/8.72 (* end of lemma zenon_L254_ *) % 8.54/8.72 assert (zenon_L255_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H285 zenon_H145 zenon_Hac zenon_H192 zenon_H78 zenon_H282 zenon_H12b zenon_H66 zenon_H137 zenon_H173 zenon_H3b zenon_H1a9 zenon_H27f. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H143 | zenon_intro zenon_H286 ]. % 8.54/8.72 apply (zenon_L248_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H165 | zenon_intro zenon_H287 ]. % 8.54/8.72 apply (zenon_L252_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H80 | zenon_intro zenon_H10f ]. % 8.54/8.72 apply (zenon_L40_); trivial. % 8.54/8.72 apply (zenon_L254_); trivial. % 8.54/8.72 (* end of lemma zenon_L255_ *) % 8.54/8.72 assert (zenon_L256_ : (~((op (op (e0) (e0)) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e1)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H288 zenon_H66. % 8.54/8.72 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.54/8.72 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 8.54/8.72 congruence. % 8.54/8.72 exact (zenon_H6a zenon_H66). % 8.54/8.72 apply zenon_H3f. apply refl_equal. % 8.54/8.72 (* end of lemma zenon_L256_ *) % 8.54/8.72 assert (zenon_L257_ : ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (op (op (e0) (e0)) (e0)))) -> False). % 8.54/8.72 do 0 intro. intros zenon_Hb0 zenon_H66 zenon_H289. % 8.54/8.72 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H28a | zenon_intro zenon_H28b ]. % 8.54/8.72 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e2) = (op (op (e0) (e0)) (e0)))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H289. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H28a. % 8.54/8.72 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H28b]. % 8.54/8.72 cut (((op (op (e0) (e0)) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H28c]. % 8.54/8.72 congruence. % 8.54/8.72 cut (((op (e1) (e0)) = (e2)) = ((op (op (e0) (e0)) (e0)) = (e2))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H28c. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_Hb0. % 8.54/8.72 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.72 cut (((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H28d]. % 8.54/8.72 congruence. % 8.54/8.72 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H28a | zenon_intro zenon_H28b ]. % 8.54/8.72 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H28d. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H28a. % 8.54/8.72 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H28b]. % 8.54/8.72 cut (((op (op (e0) (e0)) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H288]. % 8.54/8.72 congruence. % 8.54/8.72 apply (zenon_L256_); trivial. % 8.54/8.72 apply zenon_H28b. apply refl_equal. % 8.54/8.72 apply zenon_H28b. apply refl_equal. % 8.54/8.72 apply zenon_H4b. apply refl_equal. % 8.54/8.72 apply zenon_H28b. apply refl_equal. % 8.54/8.72 apply zenon_H28b. apply refl_equal. % 8.54/8.72 (* end of lemma zenon_L257_ *) % 8.54/8.72 assert (zenon_L258_ : ((op (e2) (e1)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H196 zenon_Hb0 zenon_H66. % 8.54/8.72 apply (zenon_notand_s _ _ ax13); [ zenon_intro zenon_H72 | zenon_intro zenon_H28e ]. % 8.54/8.72 apply zenon_H72. apply sym_equal. exact zenon_H66. % 8.54/8.72 apply (zenon_notand_s _ _ zenon_H28e); [ zenon_intro zenon_H28f | zenon_intro zenon_H289 ]. % 8.54/8.72 elim (classic ((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H290 | zenon_intro zenon_H291 ]. % 8.54/8.72 cut (((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0)))) = ((e3) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H28f. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H290. % 8.54/8.72 cut (((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H291]. % 8.54/8.72 cut (((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H292]. % 8.54/8.72 congruence. % 8.54/8.72 cut (((op (e2) (e1)) = (e3)) = ((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (e3))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H292. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H196. % 8.54/8.72 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.72 cut (((op (e2) (e1)) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H293]. % 8.54/8.72 congruence. % 8.54/8.72 elim (classic ((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H290 | zenon_intro zenon_H291 ]. % 8.54/8.72 cut (((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0)))) = ((op (e2) (e1)) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H293. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H290. % 8.54/8.72 cut (((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H291]. % 8.54/8.72 cut (((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H294]. % 8.54/8.72 congruence. % 8.54/8.72 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 8.54/8.72 cut (((op (op (e0) (e0)) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H28c]. % 8.54/8.72 congruence. % 8.54/8.72 cut (((op (e1) (e0)) = (e2)) = ((op (op (e0) (e0)) (e0)) = (e2))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H28c. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_Hb0. % 8.54/8.72 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.72 cut (((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H28d]. % 8.54/8.72 congruence. % 8.54/8.72 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H28a | zenon_intro zenon_H28b ]. % 8.54/8.72 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H28d. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H28a. % 8.54/8.72 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H28b]. % 8.54/8.72 cut (((op (op (e0) (e0)) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H288]. % 8.54/8.72 congruence. % 8.54/8.72 apply (zenon_L256_); trivial. % 8.54/8.72 apply zenon_H28b. apply refl_equal. % 8.54/8.72 apply zenon_H28b. apply refl_equal. % 8.54/8.72 apply zenon_H4b. apply refl_equal. % 8.54/8.72 exact (zenon_H6a zenon_H66). % 8.54/8.72 apply zenon_H291. apply refl_equal. % 8.54/8.72 apply zenon_H291. apply refl_equal. % 8.54/8.72 apply zenon_H58. apply refl_equal. % 8.54/8.72 apply zenon_H291. apply refl_equal. % 8.54/8.72 apply zenon_H291. apply refl_equal. % 8.54/8.72 apply (zenon_L257_); trivial. % 8.54/8.72 (* end of lemma zenon_L258_ *) % 8.54/8.72 assert (zenon_L259_ : ((op (e3) (e0)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H1a9 zenon_H87 zenon_H295. % 8.54/8.72 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H271 | zenon_intro zenon_H172 ]. % 8.54/8.72 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e1) (e0)) = (op (e3) (e0)))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H295. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H271. % 8.54/8.72 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 8.54/8.72 cut (((op (e3) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H296]. % 8.54/8.72 congruence. % 8.54/8.72 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e1) (e0)))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H296. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H1a9. % 8.54/8.72 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 8.54/8.72 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 8.54/8.72 congruence. % 8.54/8.72 apply zenon_H172. apply refl_equal. % 8.54/8.72 apply zenon_Hb6. apply sym_equal. exact zenon_H87. % 8.54/8.72 apply zenon_H172. apply refl_equal. % 8.54/8.72 apply zenon_H172. apply refl_equal. % 8.54/8.72 (* end of lemma zenon_L259_ *) % 8.54/8.72 assert (zenon_L260_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e1)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> False). % 8.54/8.72 do 0 intro. intros zenon_Hb7 zenon_H27f zenon_H3b zenon_H173 zenon_H137 zenon_H12b zenon_H282 zenon_H78 zenon_H192 zenon_H145 zenon_H285 zenon_Hb4 zenon_H35 zenon_H66 zenon_H196 zenon_H1a9 zenon_H295. % 8.54/8.72 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hac | zenon_intro zenon_Hb8 ]. % 8.54/8.72 apply (zenon_L255_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb9 ]. % 8.54/8.72 apply (zenon_L119_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H87 ]. % 8.54/8.72 apply (zenon_L258_); trivial. % 8.54/8.72 apply (zenon_L259_); trivial. % 8.54/8.72 (* end of lemma zenon_L260_ *) % 8.54/8.72 assert (zenon_L261_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H143 zenon_Hc9 zenon_H67. % 8.54/8.72 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H68 | zenon_intro zenon_H40 ]. % 8.54/8.72 cut (((e1) = (e1)) = ((e0) = (e1))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H67. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H68. % 8.54/8.72 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.54/8.72 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 8.54/8.72 congruence. % 8.54/8.72 cut (((op (e2) (e0)) = (e0)) = ((e1) = (e0))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H69. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H143. % 8.54/8.72 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.54/8.72 cut (((op (e2) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 8.54/8.72 congruence. % 8.54/8.72 exact (zenon_Hca zenon_Hc9). % 8.54/8.72 apply zenon_H3f. apply refl_equal. % 8.54/8.72 apply zenon_H40. apply refl_equal. % 8.54/8.72 apply zenon_H40. apply refl_equal. % 8.54/8.72 (* end of lemma zenon_L261_ *) % 8.54/8.72 assert (zenon_L262_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H150 zenon_H25 zenon_H71 zenon_Hb4 zenon_H35 zenon_H67 zenon_H143 zenon_Ha3 zenon_H1a9. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.54/8.72 apply (zenon_L19_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.54/8.72 apply (zenon_L119_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.54/8.72 apply (zenon_L261_); trivial. % 8.54/8.72 apply (zenon_L158_); trivial. % 8.54/8.72 (* end of lemma zenon_L262_ *) % 8.54/8.72 assert (zenon_L263_ : (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H67 zenon_H35 zenon_Hd1. % 8.54/8.72 cut (((op (e1) (e3)) = (e1)) = ((e0) = (e1))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H67. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H35. % 8.54/8.72 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.54/8.72 cut (((op (e1) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H297]. % 8.54/8.72 congruence. % 8.54/8.72 exact (zenon_H297 zenon_Hd1). % 8.54/8.72 apply zenon_H40. apply refl_equal. % 8.54/8.72 (* end of lemma zenon_L263_ *) % 8.54/8.72 assert (zenon_L264_ : (~((op (e3) (op (e3) (e3))) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H59 zenon_H1a9 zenon_Hd4. % 8.54/8.72 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (op (e3) (e3))) = (e3))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H59. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H1a9. % 8.54/8.72 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.72 cut (((op (e3) (e0)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H298]. % 8.54/8.72 congruence. % 8.54/8.72 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 8.54/8.72 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((op (e3) (e0)) = (op (e3) (op (e3) (e3))))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H298. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H5c. % 8.54/8.72 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 8.54/8.72 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H299]. % 8.54/8.72 congruence. % 8.54/8.72 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 8.54/8.72 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.72 congruence. % 8.54/8.72 apply zenon_H58. apply refl_equal. % 8.54/8.72 exact (zenon_Hd5 zenon_Hd4). % 8.54/8.72 apply zenon_H5d. apply refl_equal. % 8.54/8.72 apply zenon_H5d. apply refl_equal. % 8.54/8.72 apply zenon_H58. apply refl_equal. % 8.54/8.72 (* end of lemma zenon_L264_ *) % 8.54/8.72 assert (zenon_L265_ : (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e3) (e1)) = (e1)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H64 zenon_Hf4. % 8.54/8.72 cut (((op (e3) (e1)) = (e1)) = ((op (e3) (op (e3) (e1))) = (e1))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H64. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_Hf4. % 8.54/8.72 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.54/8.72 cut (((op (e3) (e1)) = (op (e3) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H29a]. % 8.54/8.72 congruence. % 8.54/8.72 elim (classic ((op (e3) (op (e3) (e1))) = (op (e3) (op (e3) (e1))))); [ zenon_intro zenon_H29b | zenon_intro zenon_H29c ]. % 8.54/8.72 cut (((op (e3) (op (e3) (e1))) = (op (e3) (op (e3) (e1)))) = ((op (e3) (e1)) = (op (e3) (op (e3) (e1))))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H29a. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H29b. % 8.54/8.72 cut (((op (e3) (op (e3) (e1))) = (op (e3) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H29c]. % 8.54/8.72 cut (((op (e3) (op (e3) (e1))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H29d]. % 8.54/8.72 congruence. % 8.54/8.72 cut (((op (e3) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H29e]. % 8.54/8.72 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.72 congruence. % 8.54/8.72 apply zenon_H58. apply refl_equal. % 8.54/8.72 exact (zenon_H29e zenon_Hf4). % 8.54/8.72 apply zenon_H29c. apply refl_equal. % 8.54/8.72 apply zenon_H29c. apply refl_equal. % 8.54/8.72 apply zenon_H40. apply refl_equal. % 8.54/8.72 (* end of lemma zenon_L265_ *) % 8.54/8.72 assert (zenon_L266_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H29f zenon_H71 zenon_Hf6. % 8.54/8.72 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H29f. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H71. % 8.54/8.72 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2a0]. % 8.54/8.72 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 8.54/8.72 congruence. % 8.54/8.72 apply zenon_H27. apply refl_equal. % 8.54/8.72 apply zenon_H2a0. apply sym_equal. exact zenon_Hf6. % 8.54/8.72 (* end of lemma zenon_L266_ *) % 8.54/8.72 assert (zenon_L267_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H16d zenon_H35 zenon_He5. % 8.54/8.72 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e3) (e3)))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H16d. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H35. % 8.54/8.72 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He6]. % 8.54/8.72 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 8.54/8.72 congruence. % 8.54/8.72 apply zenon_H38. apply refl_equal. % 8.54/8.72 apply zenon_He6. apply sym_equal. exact zenon_He5. % 8.54/8.72 (* end of lemma zenon_L267_ *) % 8.54/8.72 assert (zenon_L268_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.54/8.72 do 0 intro. intros zenon_Hf9 zenon_H1a9 zenon_Ha3 zenon_H64 zenon_H71 zenon_H29f zenon_H16d zenon_H35. % 8.54/8.72 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hfc ]. % 8.54/8.72 apply (zenon_L158_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hfd ]. % 8.54/8.72 apply (zenon_L265_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_Hf6 | zenon_intro zenon_He5 ]. % 8.54/8.72 apply (zenon_L266_); trivial. % 8.54/8.72 apply (zenon_L267_); trivial. % 8.54/8.72 (* end of lemma zenon_L268_ *) % 8.54/8.72 assert (zenon_L269_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H22d zenon_Hd0 zenon_Hf9 zenon_Ha3 zenon_H29f zenon_H16d zenon_H1d zenon_H67 zenon_H11f zenon_H127 zenon_H27f zenon_H173 zenon_H137 zenon_H12b zenon_H282 zenon_H2a1 zenon_H2a2 zenon_H1f zenon_H150 zenon_H25 zenon_Hb4 zenon_H2a3 zenon_H295 zenon_H285 zenon_H145 zenon_H192 zenon_H78 zenon_Hb7 zenon_H1d3 zenon_Hc2 zenon_H270 zenon_H2a4 zenon_H2a5 zenon_H3b zenon_H3a zenon_H1d7 zenon_H1a9. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.54/8.72 apply (zenon_L73_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H118. zenon_intro zenon_H18a. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.54/8.72 apply (zenon_L76_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.54/8.72 apply (zenon_L77_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2a4); [ zenon_intro zenon_H26f | zenon_intro zenon_H2ad ]. % 8.54/8.72 apply (zenon_L243_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H274 | zenon_intro zenon_H2ae ]. % 8.54/8.72 apply (zenon_L244_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H276 | zenon_intro zenon_H103 ]. % 8.54/8.72 apply (zenon_L245_); trivial. % 8.54/8.72 apply (zenon_L123_); trivial. % 8.54/8.72 apply (zenon_L246_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H41. zenon_intro zenon_H4a. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.54/8.72 apply (zenon_L1_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.54/8.72 apply (zenon_L82_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2a3); [ zenon_intro zenon_H274 | zenon_intro zenon_H2b2 ]. % 8.54/8.72 apply (zenon_L244_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H2b3 ]. % 8.54/8.72 apply (zenon_L247_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H196 | zenon_intro zenon_H1b1 ]. % 8.54/8.72 apply (zenon_L260_); trivial. % 8.54/8.72 apply (zenon_L165_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.54/8.72 apply (zenon_L77_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.54/8.72 apply (zenon_L262_); trivial. % 8.54/8.72 apply (zenon_L246_); trivial. % 8.54/8.72 apply (zenon_L133_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.54/8.72 apply (zenon_L13_); trivial. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H59. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.54/8.72 apply (zenon_L73_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.54/8.72 apply (zenon_L263_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.54/8.72 apply (zenon_L254_); trivial. % 8.54/8.72 apply (zenon_L264_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.54/8.72 apply (zenon_L77_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.54/8.72 apply (zenon_L268_); trivial. % 8.54/8.72 apply (zenon_L246_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.54/8.72 apply (zenon_L6_); trivial. % 8.54/8.72 apply (zenon_L169_); trivial. % 8.54/8.72 (* end of lemma zenon_L269_ *) % 8.54/8.72 assert (zenon_L270_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H201 zenon_H22d zenon_Hd0 zenon_Hf9 zenon_Ha3 zenon_H29f zenon_H16d zenon_H1d zenon_H67 zenon_H11f zenon_H127 zenon_H27f zenon_H173 zenon_H137 zenon_H12b zenon_H282 zenon_H2a1 zenon_H2a2 zenon_H1f zenon_H150 zenon_H25 zenon_Hb4 zenon_H2a3 zenon_H295 zenon_H285 zenon_H145 zenon_H192 zenon_H78 zenon_Hb7 zenon_H1d3 zenon_Hc2 zenon_H270 zenon_H2a4 zenon_H2a5 zenon_H3a zenon_H1d7 zenon_H1a9. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H201). zenon_intro zenon_H3b. zenon_intro zenon_H202. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H202). zenon_intro zenon_H3b. zenon_intro zenon_H1a5. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1a5). zenon_intro zenon_H3b. zenon_intro zenon_H3b. % 8.54/8.72 apply (zenon_L269_); trivial. % 8.54/8.72 (* end of lemma zenon_L270_ *) % 8.54/8.72 assert (zenon_L271_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H203 zenon_H3a. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H203). zenon_intro zenon_H3b. zenon_intro zenon_H204. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H204). zenon_intro zenon_H3b. zenon_intro zenon_H1a8. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hbd. zenon_intro zenon_H3c. % 8.54/8.72 apply (zenon_L6_); trivial. % 8.54/8.72 (* end of lemma zenon_L271_ *) % 8.54/8.72 assert (zenon_L272_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H203 zenon_H3a. % 8.54/8.72 apply (zenon_L271_); trivial. % 8.54/8.72 (* end of lemma zenon_L272_ *) % 8.54/8.72 assert (zenon_L273_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e0) (op (e0) (e3))) = (e3))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H205 zenon_H18a. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H3c. zenon_intro zenon_H206. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_Hbd. zenon_intro zenon_H1ad. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H103. zenon_intro zenon_H1a9. % 8.54/8.72 apply (zenon_L123_); trivial. % 8.54/8.72 (* end of lemma zenon_L273_ *) % 8.54/8.72 assert (zenon_L274_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H20d zenon_H1d zenon_H1f. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H20d). zenon_intro zenon_H1a9. zenon_intro zenon_H20e. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H20e). zenon_intro zenon_H103. zenon_intro zenon_H177. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H1e. zenon_intro zenon_H1e. % 8.54/8.72 apply (zenon_L1_); trivial. % 8.54/8.72 (* end of lemma zenon_L274_ *) % 8.54/8.72 assert (zenon_L275_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((op (e0) (op (e0) (e3))) = (e3))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H20f zenon_H18a. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H20f). zenon_intro zenon_H1a9. zenon_intro zenon_H210. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H210). zenon_intro zenon_H103. zenon_intro zenon_H17a. % 8.54/8.72 apply (zenon_L123_); trivial. % 8.54/8.72 (* end of lemma zenon_L275_ *) % 8.54/8.72 assert (zenon_L276_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H211 zenon_H1d zenon_H124. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H211). zenon_intro zenon_H1a9. zenon_intro zenon_H212. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H212). zenon_intro zenon_H103. zenon_intro zenon_H17d. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H143. zenon_intro zenon_H24. % 8.54/8.72 apply (zenon_L72_); trivial. % 8.54/8.72 (* end of lemma zenon_L276_ *) % 8.54/8.72 assert (zenon_L277_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e1) (op (e1) (e0))) = (e0))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H187 zenon_H49. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H187). zenon_intro zenon_H1d. zenon_intro zenon_H188. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H188). zenon_intro zenon_Hac. zenon_intro zenon_H189. % 8.54/8.72 apply (zenon_L82_); trivial. % 8.54/8.72 (* end of lemma zenon_L277_ *) % 8.54/8.72 assert (zenon_L278_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H1a0 zenon_H154. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1a0). zenon_intro zenon_H24. zenon_intro zenon_H1a1. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1a1). zenon_intro zenon_H143. zenon_intro zenon_H1a2. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1a2). zenon_intro zenon_H93. zenon_intro zenon_H191. % 8.54/8.72 apply (zenon_L97_); trivial. % 8.54/8.72 (* end of lemma zenon_L278_ *) % 8.54/8.72 assert (zenon_L279_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H1fb zenon_H154. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H191. zenon_intro zenon_H1fc. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_H93. zenon_intro zenon_H1c7. % 8.54/8.72 apply (zenon_L97_); trivial. % 8.54/8.72 (* end of lemma zenon_L279_ *) % 8.54/8.72 assert (zenon_L280_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H205 zenon_H197 zenon_H191. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H3c. zenon_intro zenon_H206. % 8.54/8.72 apply (zenon_L191_); trivial. % 8.54/8.72 (* end of lemma zenon_L280_ *) % 8.54/8.72 assert (zenon_L281_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((op (e1) (op (e1) (e0))) = (e0))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H20f zenon_H49. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H20f). zenon_intro zenon_H1a9. zenon_intro zenon_H210. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H210). zenon_intro zenon_H103. zenon_intro zenon_H17a. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_Hac. zenon_intro zenon_H1d. % 8.54/8.72 apply (zenon_L82_); trivial. % 8.54/8.72 (* end of lemma zenon_L281_ *) % 8.54/8.72 assert (zenon_L282_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H17b zenon_H54. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H17b). zenon_intro zenon_H1e. zenon_intro zenon_H17c. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H17c). zenon_intro zenon_H1e. zenon_intro zenon_H17d. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H143. zenon_intro zenon_H24. % 8.54/8.72 apply (zenon_L100_); trivial. % 8.54/8.72 (* end of lemma zenon_L282_ *) % 8.54/8.72 assert (zenon_L283_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H187 zenon_H56. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H187). zenon_intro zenon_H1d. zenon_intro zenon_H188. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H188). zenon_intro zenon_Hac. zenon_intro zenon_H189. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H15a. zenon_intro zenon_H29. % 8.54/8.72 apply (zenon_L99_); trivial. % 8.54/8.72 (* end of lemma zenon_L283_ *) % 8.54/8.72 assert (zenon_L284_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H1a0 zenon_H54. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1a0). zenon_intro zenon_H24. zenon_intro zenon_H1a1. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1a1). zenon_intro zenon_H143. zenon_intro zenon_H1a2. % 8.54/8.72 apply (zenon_L100_); trivial. % 8.54/8.72 (* end of lemma zenon_L284_ *) % 8.54/8.72 assert (zenon_L285_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H1a6 zenon_H54. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1a6). zenon_intro zenon_H24. zenon_intro zenon_H1a7. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H143. zenon_intro zenon_H1a8. % 8.54/8.72 apply (zenon_L100_); trivial. % 8.54/8.72 (* end of lemma zenon_L285_ *) % 8.54/8.72 assert (zenon_L286_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H1bb zenon_H54. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1bb). zenon_intro zenon_H73. zenon_intro zenon_H1bc. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1bc). zenon_intro zenon_H6b. zenon_intro zenon_H17d. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H143. zenon_intro zenon_H24. % 8.54/8.72 apply (zenon_L100_); trivial. % 8.54/8.72 (* end of lemma zenon_L286_ *) % 8.54/8.72 assert (zenon_L287_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H1ce zenon_H56. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H29. zenon_intro zenon_H1cf. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_H15a. zenon_intro zenon_H1a8. % 8.54/8.72 apply (zenon_L99_); trivial. % 8.54/8.72 (* end of lemma zenon_L287_ *) % 8.54/8.72 assert (zenon_L288_ : (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> False). % 8.54/8.72 do 0 intro. intros zenon_Ha3 zenon_H103 zenon_Hd6. % 8.54/8.72 cut (((op (e0) (e3)) = (e3)) = ((e1) = (e3))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_Ha3. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H103. % 8.54/8.72 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.72 cut (((op (e0) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2b4]. % 8.54/8.72 congruence. % 8.54/8.72 exact (zenon_H2b4 zenon_Hd6). % 8.54/8.72 apply zenon_H58. apply refl_equal. % 8.54/8.72 (* end of lemma zenon_L288_ *) % 8.54/8.72 assert (zenon_L289_ : (((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 (e2) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H2b5 zenon_Hac zenon_Hb4 zenon_H16b zenon_H109 zenon_H3c zenon_Hd0 zenon_H103. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H2b6 ]. % 8.54/8.72 apply (zenon_L105_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H35 | zenon_intro zenon_H2b7 ]. % 8.54/8.72 apply (zenon_L106_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H108 | zenon_intro zenon_Hb3 ]. % 8.54/8.72 apply (zenon_L63_); trivial. % 8.54/8.72 apply (zenon_L60_); trivial. % 8.54/8.72 (* end of lemma zenon_L289_ *) % 8.54/8.72 assert (zenon_L290_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((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)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H2b8 zenon_Ha3 zenon_H29 zenon_H129 zenon_H2b5 zenon_Hac zenon_Hb4 zenon_H16d zenon_H109 zenon_H3c zenon_Hd0 zenon_H103. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H2b9 ]. % 8.54/8.72 apply (zenon_L288_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_H35 | zenon_intro zenon_H2ba ]. % 8.54/8.72 apply (zenon_L74_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H16b | zenon_intro zenon_He5 ]. % 8.54/8.72 apply (zenon_L289_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H2b6 ]. % 8.54/8.72 apply (zenon_L105_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H35 | zenon_intro zenon_H2b7 ]. % 8.54/8.72 apply (zenon_L267_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H108 | zenon_intro zenon_Hb3 ]. % 8.54/8.72 apply (zenon_L63_); trivial. % 8.54/8.72 apply (zenon_L60_); trivial. % 8.54/8.72 (* end of lemma zenon_L290_ *) % 8.54/8.72 assert (zenon_L291_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H2a2 zenon_H1f zenon_H1d zenon_H103 zenon_Hd0 zenon_H3c zenon_H109 zenon_H16d zenon_Hb4 zenon_H2b5 zenon_H129 zenon_H29 zenon_Ha3 zenon_H2b8 zenon_H54 zenon_Hc2 zenon_H1a9. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.54/8.72 apply (zenon_L1_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.54/8.72 apply (zenon_L290_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.54/8.72 apply (zenon_L100_); trivial. % 8.54/8.72 apply (zenon_L133_); trivial. % 8.54/8.72 (* end of lemma zenon_L291_ *) % 8.54/8.72 assert (zenon_L292_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H20f zenon_H2b8 zenon_Ha3 zenon_H29 zenon_H129 zenon_H2b5 zenon_Hb4 zenon_H16d zenon_H109 zenon_H3c zenon_Hd0. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H20f). zenon_intro zenon_H1a9. zenon_intro zenon_H210. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H210). zenon_intro zenon_H103. zenon_intro zenon_H17a. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_Hac. zenon_intro zenon_H1d. % 8.54/8.72 apply (zenon_L290_); trivial. % 8.54/8.72 (* end of lemma zenon_L292_ *) % 8.54/8.72 assert (zenon_L293_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((op (e2) (op (e2) (e0))) = (e0))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H211 zenon_H54. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H211). zenon_intro zenon_H1a9. zenon_intro zenon_H212. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H212). zenon_intro zenon_H103. zenon_intro zenon_H17d. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H143. zenon_intro zenon_H24. % 8.54/8.72 apply (zenon_L100_); trivial. % 8.54/8.72 (* end of lemma zenon_L293_ *) % 8.54/8.72 assert (zenon_L294_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H11f zenon_H1d zenon_H127 zenon_Hac zenon_Hb4 zenon_H3c zenon_H78 zenon_H59 zenon_H1a9. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.54/8.72 apply (zenon_L73_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.54/8.72 apply (zenon_L105_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.54/8.72 apply (zenon_L65_); trivial. % 8.54/8.72 apply (zenon_L264_); trivial. % 8.54/8.72 (* end of lemma zenon_L294_ *) % 8.54/8.72 assert (zenon_L295_ : (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e3) (e2)) = (e2)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H65 zenon_Hbd. % 8.54/8.72 cut (((op (e3) (e2)) = (e2)) = ((op (e3) (op (e3) (e2))) = (e2))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H65. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_Hbd. % 8.54/8.72 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.72 cut (((op (e3) (e2)) = (op (e3) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2bb]. % 8.54/8.72 congruence. % 8.54/8.72 elim (classic ((op (e3) (op (e3) (e2))) = (op (e3) (op (e3) (e2))))); [ zenon_intro zenon_H2bc | zenon_intro zenon_H2bd ]. % 8.54/8.72 cut (((op (e3) (op (e3) (e2))) = (op (e3) (op (e3) (e2)))) = ((op (e3) (e2)) = (op (e3) (op (e3) (e2))))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H2bb. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H2bc. % 8.54/8.72 cut (((op (e3) (op (e3) (e2))) = (op (e3) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2bd]. % 8.54/8.72 cut (((op (e3) (op (e3) (e2))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2be]. % 8.54/8.72 congruence. % 8.54/8.72 cut (((op (e3) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 8.54/8.72 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.72 congruence. % 8.54/8.72 apply zenon_H58. apply refl_equal. % 8.54/8.72 exact (zenon_Hbe zenon_Hbd). % 8.54/8.72 apply zenon_H2bd. apply refl_equal. % 8.54/8.72 apply zenon_H2bd. apply refl_equal. % 8.54/8.72 apply zenon_H4b. apply refl_equal. % 8.54/8.72 (* end of lemma zenon_L295_ *) % 8.54/8.72 assert (zenon_L296_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H1a6 zenon_H65. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1a6). zenon_intro zenon_H24. zenon_intro zenon_H1a7. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H143. zenon_intro zenon_H1a8. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hbd. zenon_intro zenon_H3c. % 8.54/8.72 apply (zenon_L295_); trivial. % 8.54/8.72 (* end of lemma zenon_L296_ *) % 8.54/8.72 assert (zenon_L297_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H1ce zenon_H65. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H29. zenon_intro zenon_H1cf. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_H15a. zenon_intro zenon_H1a8. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hbd. zenon_intro zenon_H3c. % 8.54/8.72 apply (zenon_L295_); trivial. % 8.54/8.72 (* end of lemma zenon_L297_ *) % 8.54/8.72 assert (zenon_L298_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H1e2 zenon_H64. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1e2). zenon_intro zenon_H35. zenon_intro zenon_H1e3. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1e3). zenon_intro zenon_Hf4. zenon_intro zenon_H1ad. % 8.54/8.72 apply (zenon_L265_); trivial. % 8.54/8.72 (* end of lemma zenon_L298_ *) % 8.54/8.72 assert (zenon_L299_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H203 zenon_H65. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H203). zenon_intro zenon_H3b. zenon_intro zenon_H204. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H204). zenon_intro zenon_H3b. zenon_intro zenon_H1a8. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hbd. zenon_intro zenon_H3c. % 8.54/8.72 apply (zenon_L295_); trivial. % 8.54/8.72 (* end of lemma zenon_L299_ *) % 8.54/8.72 assert (zenon_L300_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> False). % 8.54/8.72 do 0 intro. intros zenon_H205 zenon_H65. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H3c. zenon_intro zenon_H206. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_Hbd. zenon_intro zenon_H1ad. % 8.54/8.72 apply (zenon_L295_); trivial. % 8.54/8.72 (* end of lemma zenon_L300_ *) % 8.54/8.72 assert (zenon_L301_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H11f zenon_Hc2 zenon_H103 zenon_Hac zenon_Hb4 zenon_H3c zenon_H78 zenon_H59 zenon_H1a9. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.54/8.72 apply (zenon_L201_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.54/8.72 apply (zenon_L105_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.54/8.72 apply (zenon_L65_); trivial. % 8.54/8.72 apply (zenon_L264_); trivial. % 8.54/8.72 (* end of lemma zenon_L301_ *) % 8.54/8.72 assert (zenon_L302_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H2bf zenon_H1dc zenon_H1dd zenon_H169 zenon_H2c0 zenon_H1d9 zenon_H2b8 zenon_H2b5 zenon_H109 zenon_H197 zenon_H22e zenon_H31 zenon_Hab zenon_H2b zenon_H7d zenon_H129 zenon_H1f6 zenon_H124 zenon_H1d7 zenon_H3a zenon_H2a5 zenon_H2a4 zenon_H270 zenon_Hc2 zenon_H1d3 zenon_Hb7 zenon_H78 zenon_H192 zenon_H145 zenon_H285 zenon_H295 zenon_H2a3 zenon_Hb4 zenon_H25 zenon_H150 zenon_H1f zenon_H2a2 zenon_H2a1 zenon_H282 zenon_H12b zenon_H137 zenon_H173 zenon_H27f zenon_H127 zenon_H11f zenon_H67 zenon_H1d zenon_H16d zenon_H29f zenon_Ha3 zenon_Hf9 zenon_Hd0 zenon_H22d zenon_H170 zenon_H1a9. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c1 ]. % 8.54/8.72 apply (zenon_L72_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H29 | zenon_intro zenon_H2c2 ]. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.54/8.72 apply (zenon_L73_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.54/8.72 apply (zenon_L74_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H118. zenon_intro zenon_H18a. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.72 apply (zenon_L113_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.72 apply (zenon_L114_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.72 apply (zenon_L116_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.72 apply (zenon_L154_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.72 apply (zenon_L155_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.72 apply (zenon_L156_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H187). zenon_intro zenon_H1d. zenon_intro zenon_H188. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H188). zenon_intro zenon_Hac. zenon_intro zenon_H189. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H15a. zenon_intro zenon_H29. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.54/8.72 apply (zenon_L76_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.54/8.72 apply (zenon_L93_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.54/8.72 apply (zenon_L157_); trivial. % 8.54/8.72 apply (zenon_L158_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.72 apply (zenon_L159_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.72 apply (zenon_L160_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.72 apply (zenon_L162_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.72 apply (zenon_L163_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.72 apply (zenon_L164_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.72 apply (zenon_L134_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.72 apply (zenon_L166_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.72 apply (zenon_L168_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.72 apply (zenon_L170_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.72 apply (zenon_L171_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.72 apply (zenon_L172_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.72 apply (zenon_L173_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.72 apply (zenon_L174_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.72 apply (zenon_L175_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.72 apply (zenon_L176_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.72 apply (zenon_L146_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.72 apply (zenon_L177_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.72 apply (zenon_L178_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.72 apply (zenon_L151_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.72 apply (zenon_L179_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H29. zenon_intro zenon_H1cf. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_H15a. zenon_intro zenon_H1a8. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hbd. zenon_intro zenon_H3c. % 8.54/8.72 apply (zenon_L181_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.72 apply (zenon_L182_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.72 apply (zenon_L183_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.72 apply (zenon_L184_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.72 apply (zenon_L185_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.72 apply (zenon_L186_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.72 apply (zenon_L187_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.72 apply (zenon_L188_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.72 apply (zenon_L189_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.72 apply (zenon_L190_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.72 apply (zenon_L192_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.72 apply (zenon_L240_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.72 apply (zenon_L214_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.72 apply (zenon_L241_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.72 apply (zenon_L242_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.72 apply (zenon_L270_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.72 apply (zenon_L272_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.72 apply (zenon_L273_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.72 apply (zenon_L220_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.72 apply (zenon_L221_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.72 apply (zenon_L222_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.72 apply (zenon_L274_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.72 apply (zenon_L275_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.72 apply (zenon_L276_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.72 apply (zenon_L226_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.72 apply (zenon_L227_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.72 apply (zenon_L228_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.72 apply (zenon_L229_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.72 apply (zenon_L230_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.72 apply (zenon_L231_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.72 apply (zenon_L232_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.72 apply (zenon_L233_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.72 apply (zenon_L234_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.72 apply (zenon_L235_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.72 apply (zenon_L236_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.72 apply (zenon_L237_); trivial. % 8.54/8.72 apply (zenon_L238_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H41. zenon_intro zenon_H4a. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H4a). zenon_intro zenon_H154. zenon_intro zenon_H2c3. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.72 apply (zenon_L113_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.72 apply (zenon_L114_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.72 apply (zenon_L116_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.72 apply (zenon_L154_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.72 apply (zenon_L155_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.72 apply (zenon_L156_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.72 apply (zenon_L277_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.72 apply (zenon_L159_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.72 apply (zenon_L160_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.72 apply (zenon_L278_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.72 apply (zenon_L163_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.72 apply (zenon_L164_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.72 apply (zenon_L134_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.72 apply (zenon_L166_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.72 apply (zenon_L168_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.72 apply (zenon_L170_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.72 apply (zenon_L171_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.72 apply (zenon_L172_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.72 apply (zenon_L173_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.72 apply (zenon_L174_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.72 apply (zenon_L175_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.72 apply (zenon_L176_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.72 apply (zenon_L146_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.72 apply (zenon_L177_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.72 apply (zenon_L178_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.72 apply (zenon_L205_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.72 apply (zenon_L179_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H29. zenon_intro zenon_H1cf. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_H15a. zenon_intro zenon_H1a8. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hbd. zenon_intro zenon_H3c. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_Hcb | zenon_intro zenon_H2c4 ]. % 8.54/8.72 apply (zenon_L80_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H2c5 ]. % 8.54/8.72 apply (zenon_L85_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1d8 ]. % 8.54/8.72 apply (zenon_L149_); trivial. % 8.54/8.72 apply (zenon_L180_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.72 apply (zenon_L182_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.72 apply (zenon_L183_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.72 apply (zenon_L184_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.72 apply (zenon_L185_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.72 apply (zenon_L186_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.72 apply (zenon_L187_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.72 apply (zenon_L188_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.72 apply (zenon_L189_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.72 apply (zenon_L190_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.72 apply (zenon_L212_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.72 apply (zenon_L240_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.72 apply (zenon_L279_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.72 apply (zenon_L241_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.72 apply (zenon_L242_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.72 apply (zenon_L270_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.72 apply (zenon_L272_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H3c. zenon_intro zenon_H206. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_Hbd. zenon_intro zenon_H1ad. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_Hcb | zenon_intro zenon_H2c4 ]. % 8.54/8.72 apply (zenon_L80_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H2c5 ]. % 8.54/8.72 apply (zenon_L85_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1d8 ]. % 8.54/8.72 apply (zenon_L280_); trivial. % 8.54/8.72 apply (zenon_L180_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.72 apply (zenon_L220_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.72 apply (zenon_L221_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.72 apply (zenon_L222_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.72 apply (zenon_L274_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.72 apply (zenon_L281_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.72 apply (zenon_L276_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.72 apply (zenon_L226_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.72 apply (zenon_L227_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.72 apply (zenon_L228_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.72 apply (zenon_L229_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.72 apply (zenon_L230_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.72 apply (zenon_L231_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.72 apply (zenon_L232_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.72 apply (zenon_L233_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.72 apply (zenon_L234_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.72 apply (zenon_L235_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.72 apply (zenon_L236_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.72 apply (zenon_L237_); trivial. % 8.54/8.72 apply (zenon_L238_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.72 apply (zenon_L113_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.72 apply (zenon_L114_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.72 apply (zenon_L282_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.72 apply (zenon_L154_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.72 apply (zenon_L155_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.72 apply (zenon_L156_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.72 apply (zenon_L283_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.72 apply (zenon_L159_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.72 apply (zenon_L160_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.72 apply (zenon_L284_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.72 apply (zenon_L163_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.72 apply (zenon_L285_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.72 apply (zenon_L134_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.72 apply (zenon_L166_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.72 apply (zenon_L168_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.72 apply (zenon_L170_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.72 apply (zenon_L171_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.72 apply (zenon_L172_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.72 apply (zenon_L286_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.72 apply (zenon_L174_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.72 apply (zenon_L175_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.72 apply (zenon_L176_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.72 apply (zenon_L146_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.72 apply (zenon_L177_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.72 apply (zenon_L178_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.72 apply (zenon_L151_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.72 apply (zenon_L179_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.72 apply (zenon_L287_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1e2). zenon_intro zenon_H35. zenon_intro zenon_H1e3. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1e3). zenon_intro zenon_Hf4. zenon_intro zenon_H1ad. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H103. zenon_intro zenon_H1a9. % 8.54/8.72 apply (zenon_L291_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.72 apply (zenon_L183_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.72 apply (zenon_L184_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.72 apply (zenon_L185_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.72 apply (zenon_L186_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.72 apply (zenon_L187_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.72 apply (zenon_L188_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.72 apply (zenon_L189_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.72 apply (zenon_L190_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.72 apply (zenon_L192_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.72 apply (zenon_L240_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.72 apply (zenon_L214_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.72 apply (zenon_L241_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.72 apply (zenon_L242_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.72 apply (zenon_L270_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.72 apply (zenon_L272_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H3c. zenon_intro zenon_H206. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_Hbd. zenon_intro zenon_H1ad. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H103. zenon_intro zenon_H1a9. % 8.54/8.72 apply (zenon_L291_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.72 apply (zenon_L220_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.72 apply (zenon_L221_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.72 apply (zenon_L222_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.72 apply (zenon_L274_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.72 apply (zenon_L292_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.72 apply (zenon_L293_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.72 apply (zenon_L226_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.72 apply (zenon_L227_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.72 apply (zenon_L228_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.72 apply (zenon_L229_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.72 apply (zenon_L230_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.72 apply (zenon_L231_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.72 apply (zenon_L232_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.72 apply (zenon_L233_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.72 apply (zenon_L234_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.72 apply (zenon_L235_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.72 apply (zenon_L236_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.72 apply (zenon_L237_); trivial. % 8.54/8.72 apply (zenon_L238_); trivial. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H59. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.72 apply (zenon_L113_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H178). zenon_intro zenon_H1e. zenon_intro zenon_H179. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H179). zenon_intro zenon_H1e. zenon_intro zenon_H17a. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_Hac. zenon_intro zenon_H1d. % 8.54/8.72 apply (zenon_L294_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.72 apply (zenon_L116_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.72 apply (zenon_L154_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.72 apply (zenon_L155_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.72 apply (zenon_L156_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H187). zenon_intro zenon_H1d. zenon_intro zenon_H188. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H188). zenon_intro zenon_Hac. zenon_intro zenon_H189. % 8.54/8.72 apply (zenon_L294_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.72 apply (zenon_L159_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.72 apply (zenon_L160_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.72 apply (zenon_L162_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.72 apply (zenon_L163_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.72 apply (zenon_L296_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.72 apply (zenon_L134_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.72 apply (zenon_L166_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.72 apply (zenon_L168_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.72 apply (zenon_L170_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.72 apply (zenon_L171_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.72 apply (zenon_L172_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.72 apply (zenon_L173_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.72 apply (zenon_L174_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.72 apply (zenon_L175_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.72 apply (zenon_L176_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.72 apply (zenon_L146_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.72 apply (zenon_L177_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.72 apply (zenon_L178_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.72 apply (zenon_L205_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.72 apply (zenon_L179_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.72 apply (zenon_L297_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.72 apply (zenon_L298_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.72 apply (zenon_L183_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.72 apply (zenon_L184_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.72 apply (zenon_L185_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.72 apply (zenon_L186_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.72 apply (zenon_L187_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.72 apply (zenon_L188_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.72 apply (zenon_L189_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.72 apply (zenon_L190_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.72 apply (zenon_L212_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.72 apply (zenon_L240_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.72 apply (zenon_L214_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.72 apply (zenon_L241_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.72 apply (zenon_L242_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.72 apply (zenon_L270_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.72 apply (zenon_L299_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.72 apply (zenon_L300_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.72 apply (zenon_L220_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.72 apply (zenon_L221_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.72 apply (zenon_L222_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.72 apply (zenon_L274_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H20f). zenon_intro zenon_H1a9. zenon_intro zenon_H210. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H210). zenon_intro zenon_H103. zenon_intro zenon_H17a. % 8.54/8.72 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_Hac. zenon_intro zenon_H1d. % 8.54/8.72 apply (zenon_L301_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.72 apply (zenon_L276_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.72 apply (zenon_L226_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.72 apply (zenon_L227_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.72 apply (zenon_L228_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.72 apply (zenon_L229_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.72 apply (zenon_L230_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.72 apply (zenon_L231_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.72 apply (zenon_L232_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.72 apply (zenon_L233_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.72 apply (zenon_L234_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.72 apply (zenon_L235_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.72 apply (zenon_L236_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.72 apply (zenon_L237_); trivial. % 8.54/8.72 apply (zenon_L238_); trivial. % 8.54/8.72 apply (zenon_L169_); trivial. % 8.54/8.72 apply (zenon_or_s _ _ zenon_H2c2); [ zenon_intro zenon_H3b | zenon_intro zenon_H98 ]. % 8.54/8.72 apply (zenon_L269_); trivial. % 8.54/8.72 apply (zenon_L167_); trivial. % 8.54/8.72 (* end of lemma zenon_L302_ *) % 8.54/8.72 assert (zenon_L303_ : (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H153 zenon_H24 zenon_H30. % 8.54/8.72 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e0) (e3)))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H153. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H24. % 8.54/8.72 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H128]. % 8.54/8.72 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 8.54/8.72 congruence. % 8.54/8.72 apply zenon_H27. apply refl_equal. % 8.54/8.72 apply zenon_H128. apply sym_equal. exact zenon_H30. % 8.54/8.72 (* end of lemma zenon_L303_ *) % 8.54/8.72 assert (zenon_L304_ : (~((op (e0) (op (e0) (e0))) = (e0))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> False). % 8.54/8.72 do 0 intro. intros zenon_H12e zenon_H24 zenon_H77. % 8.54/8.72 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (op (e0) (e0))) = (e0))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H12e. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H24. % 8.54/8.72 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.54/8.72 cut (((op (e0) (e2)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2c6]. % 8.54/8.72 congruence. % 8.54/8.72 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H130 | zenon_intro zenon_H131 ]. % 8.54/8.72 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e2)) = (op (e0) (op (e0) (e0))))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H2c6. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H130. % 8.54/8.72 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 8.54/8.72 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2c7]. % 8.54/8.72 congruence. % 8.54/8.72 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 8.54/8.72 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.54/8.72 congruence. % 8.54/8.72 apply zenon_H3f. apply refl_equal. % 8.54/8.72 exact (zenon_H7b zenon_H77). % 8.54/8.72 apply zenon_H131. apply refl_equal. % 8.54/8.72 apply zenon_H131. apply refl_equal. % 8.54/8.72 apply zenon_H3f. apply refl_equal. % 8.54/8.72 (* end of lemma zenon_L304_ *) % 8.54/8.72 assert (zenon_L305_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 8.54/8.72 do 0 intro. intros zenon_Hac zenon_Hb0 zenon_H78. % 8.54/8.72 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H79 | zenon_intro zenon_H4b ]. % 8.54/8.72 cut (((e2) = (e2)) = ((e0) = (e2))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H78. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_H79. % 8.54/8.72 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.72 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 8.54/8.72 congruence. % 8.54/8.72 cut (((op (e1) (e0)) = (e0)) = ((e2) = (e0))). % 8.54/8.72 intro zenon_D_pnotp. % 8.54/8.72 apply zenon_H7a. % 8.54/8.72 rewrite <- zenon_D_pnotp. % 8.54/8.72 exact zenon_Hac. % 8.54/8.72 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.54/8.72 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2c8]. % 8.54/8.72 congruence. % 8.54/8.72 exact (zenon_H2c8 zenon_Hb0). % 8.54/8.72 apply zenon_H3f. apply refl_equal. % 8.54/8.72 apply zenon_H4b. apply refl_equal. % 8.54/8.72 apply zenon_H4b. apply refl_equal. % 8.54/8.72 (* end of lemma zenon_L305_ *) % 8.54/8.72 assert (zenon_L306_ : (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> False). % 8.54/8.72 do 0 intro. intros zenon_Ha8 zenon_H1a9 zenon_Hf1. % 8.54/8.73 cut (((op (e3) (e0)) = (e3)) = ((e2) = (e3))). % 8.54/8.73 intro zenon_D_pnotp. % 8.54/8.73 apply zenon_Ha8. % 8.54/8.73 rewrite <- zenon_D_pnotp. % 8.54/8.73 exact zenon_H1a9. % 8.54/8.73 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.73 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 8.54/8.73 congruence. % 8.54/8.73 exact (zenon_Hf2 zenon_Hf1). % 8.54/8.73 apply zenon_H58. apply refl_equal. % 8.54/8.73 (* end of lemma zenon_L306_ *) % 8.54/8.73 assert (zenon_L307_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> False). % 8.54/8.73 do 0 intro. intros zenon_H2c9 zenon_H2a zenon_H15a. % 8.54/8.73 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 8.54/8.73 intro zenon_D_pnotp. % 8.54/8.73 apply zenon_H2c9. % 8.54/8.73 rewrite <- zenon_D_pnotp. % 8.54/8.73 exact zenon_H2a. % 8.54/8.73 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2ca]. % 8.54/8.73 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 8.54/8.73 congruence. % 8.54/8.73 apply zenon_H6e. apply refl_equal. % 8.54/8.73 apply zenon_H2ca. apply sym_equal. exact zenon_H15a. % 8.54/8.73 (* end of lemma zenon_L307_ *) % 8.54/8.73 assert (zenon_L308_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 8.54/8.73 do 0 intro. intros zenon_H175 zenon_H24 zenon_H25. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H175). zenon_intro zenon_H1e. zenon_intro zenon_H176. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H176). zenon_intro zenon_H1e. zenon_intro zenon_H177. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H1e. zenon_intro zenon_H1e. % 8.54/8.73 apply (zenon_L2_); trivial. % 8.54/8.73 (* end of lemma zenon_L308_ *) % 8.54/8.73 assert (zenon_L309_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 8.54/8.73 do 0 intro. intros zenon_H178 zenon_H24 zenon_H124. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H178). zenon_intro zenon_H1e. zenon_intro zenon_H179. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H179). zenon_intro zenon_H1e. zenon_intro zenon_H17a. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_Hac. zenon_intro zenon_H1d. % 8.54/8.73 apply (zenon_L72_); trivial. % 8.54/8.73 (* end of lemma zenon_L309_ *) % 8.54/8.73 assert (zenon_L310_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 8.54/8.73 do 0 intro. intros zenon_H1d1 zenon_H24 zenon_H124. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1d1). zenon_intro zenon_H1d. zenon_intro zenon_H1d2. % 8.54/8.73 apply (zenon_L72_); trivial. % 8.54/8.73 (* end of lemma zenon_L310_ *) % 8.54/8.73 assert (zenon_L311_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 8.54/8.73 do 0 intro. intros zenon_H1b7 zenon_H24 zenon_H25. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_H73. zenon_intro zenon_H1b8. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1b8). zenon_intro zenon_H6b. zenon_intro zenon_H177. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H1e. zenon_intro zenon_H1e. % 8.54/8.73 apply (zenon_L2_); trivial. % 8.54/8.73 (* end of lemma zenon_L311_ *) % 8.54/8.73 assert (zenon_L312_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 8.54/8.73 do 0 intro. intros zenon_H1b9 zenon_H24 zenon_H124. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1b9). zenon_intro zenon_H73. zenon_intro zenon_H1ba. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1ba). zenon_intro zenon_H6b. zenon_intro zenon_H17a. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_Hac. zenon_intro zenon_H1d. % 8.54/8.73 apply (zenon_L72_); trivial. % 8.54/8.73 (* end of lemma zenon_L312_ *) % 8.54/8.73 assert (zenon_L313_ : ((op (e3) (e1)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 8.54/8.73 do 0 intro. intros zenon_Hf4 zenon_H6b zenon_H1dd. % 8.54/8.73 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H2cb | zenon_intro zenon_H2cc ]. % 8.54/8.73 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e0) (e1)) = (op (e3) (e1)))). % 8.54/8.73 intro zenon_D_pnotp. % 8.54/8.73 apply zenon_H1dd. % 8.54/8.73 rewrite <- zenon_D_pnotp. % 8.54/8.73 exact zenon_H2cb. % 8.54/8.73 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2cc]. % 8.54/8.73 cut (((op (e3) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2cd]. % 8.54/8.73 congruence. % 8.54/8.73 cut (((op (e3) (e1)) = (e1)) = ((op (e3) (e1)) = (op (e0) (e1)))). % 8.54/8.73 intro zenon_D_pnotp. % 8.54/8.73 apply zenon_H2cd. % 8.54/8.73 rewrite <- zenon_D_pnotp. % 8.54/8.73 exact zenon_Hf4. % 8.54/8.73 cut (((e1) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 8.54/8.73 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2cc]. % 8.54/8.73 congruence. % 8.54/8.73 apply zenon_H2cc. apply refl_equal. % 8.54/8.73 apply zenon_H70. apply sym_equal. exact zenon_H6b. % 8.54/8.73 apply zenon_H2cc. apply refl_equal. % 8.54/8.73 apply zenon_H2cc. apply refl_equal. % 8.54/8.73 (* end of lemma zenon_L313_ *) % 8.54/8.73 assert (zenon_L314_ : ((op (e2) (e1)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> False). % 8.54/8.73 do 0 intro. intros zenon_H191 zenon_Hcb zenon_H164. % 8.54/8.73 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H193 | zenon_intro zenon_H16a ]. % 8.54/8.73 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e0) (e1)) = (op (e2) (e1)))). % 8.54/8.73 intro zenon_D_pnotp. % 8.54/8.73 apply zenon_H164. % 8.54/8.73 rewrite <- zenon_D_pnotp. % 8.54/8.73 exact zenon_H193. % 8.54/8.73 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 8.54/8.73 cut (((op (e2) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2ce]. % 8.54/8.73 congruence. % 8.54/8.73 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e0) (e1)))). % 8.54/8.73 intro zenon_D_pnotp. % 8.54/8.73 apply zenon_H2ce. % 8.54/8.73 rewrite <- zenon_D_pnotp. % 8.54/8.73 exact zenon_H191. % 8.54/8.73 cut (((e2) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2cf]. % 8.54/8.73 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 8.54/8.73 congruence. % 8.54/8.73 apply zenon_H16a. apply refl_equal. % 8.54/8.73 apply zenon_H2cf. apply sym_equal. exact zenon_Hcb. % 8.54/8.73 apply zenon_H16a. apply refl_equal. % 8.54/8.73 apply zenon_H16a. apply refl_equal. % 8.54/8.73 (* end of lemma zenon_L314_ *) % 8.54/8.73 assert (zenon_L315_ : ((op (e0) (e3)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> False). % 8.54/8.73 do 0 intro. intros zenon_H103 zenon_H274 zenon_H127. % 8.54/8.73 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H32 | zenon_intro zenon_H33 ]. % 8.54/8.73 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e1)) = (op (e0) (e3)))). % 8.54/8.73 intro zenon_D_pnotp. % 8.54/8.73 apply zenon_H127. % 8.54/8.73 rewrite <- zenon_D_pnotp. % 8.54/8.73 exact zenon_H32. % 8.54/8.73 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 8.54/8.73 cut (((op (e0) (e3)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2d0]. % 8.54/8.73 congruence. % 8.54/8.73 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e0) (e1)))). % 8.54/8.73 intro zenon_D_pnotp. % 8.54/8.73 apply zenon_H2d0. % 8.54/8.73 rewrite <- zenon_D_pnotp. % 8.54/8.73 exact zenon_H103. % 8.54/8.73 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2d1]. % 8.54/8.73 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 8.54/8.73 congruence. % 8.54/8.73 apply zenon_H33. apply refl_equal. % 8.54/8.73 apply zenon_H2d1. apply sym_equal. exact zenon_H274. % 8.54/8.73 apply zenon_H33. apply refl_equal. % 8.54/8.73 apply zenon_H33. apply refl_equal. % 8.54/8.73 (* end of lemma zenon_L315_ *) % 8.54/8.73 assert (zenon_L316_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 8.54/8.73 do 0 intro. intros zenon_H1f2 zenon_H35 zenon_Hb4. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1f2). zenon_intro zenon_H191. zenon_intro zenon_H1f3. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H93. zenon_intro zenon_H183. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H183). zenon_intro zenon_H6b. zenon_intro zenon_H73. % 8.54/8.73 apply (zenon_L119_); trivial. % 8.54/8.73 (* end of lemma zenon_L316_ *) % 8.54/8.73 assert (zenon_L317_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 8.54/8.73 do 0 intro. intros zenon_H1f4 zenon_H35 zenon_H36. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1f4). zenon_intro zenon_H191. zenon_intro zenon_H1f5. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1f5). zenon_intro zenon_H93. zenon_intro zenon_H186. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H186). zenon_intro zenon_H2a. zenon_intro zenon_H2a. % 8.54/8.73 apply (zenon_L5_); trivial. % 8.54/8.73 (* end of lemma zenon_L317_ *) % 8.54/8.73 assert (zenon_L318_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 8.54/8.73 do 0 intro. intros zenon_H29f zenon_H24 zenon_Hc3. % 8.54/8.73 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 8.54/8.73 intro zenon_D_pnotp. % 8.54/8.73 apply zenon_H29f. % 8.54/8.73 rewrite <- zenon_D_pnotp. % 8.54/8.73 exact zenon_H24. % 8.54/8.73 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H171]. % 8.54/8.73 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 8.54/8.73 congruence. % 8.54/8.73 apply zenon_H27. apply refl_equal. % 8.54/8.73 apply zenon_H171. apply sym_equal. exact zenon_Hc3. % 8.54/8.73 (* end of lemma zenon_L318_ *) % 8.54/8.73 assert (zenon_L319_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 8.54/8.73 do 0 intro. intros zenon_H1d9 zenon_Hf4 zenon_Hf6. % 8.54/8.73 cut (((op (e3) (e1)) = (e1)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 8.54/8.73 intro zenon_D_pnotp. % 8.54/8.73 apply zenon_H1d9. % 8.54/8.73 rewrite <- zenon_D_pnotp. % 8.54/8.73 exact zenon_Hf4. % 8.54/8.73 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2a0]. % 8.54/8.73 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2cc]. % 8.54/8.73 congruence. % 8.54/8.73 apply zenon_H2cc. apply refl_equal. % 8.54/8.73 apply zenon_H2a0. apply sym_equal. exact zenon_Hf6. % 8.54/8.73 (* end of lemma zenon_L319_ *) % 8.54/8.73 assert (zenon_L320_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 8.54/8.73 do 0 intro. intros zenon_H2d2 zenon_H93 zenon_Hbd. % 8.54/8.73 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 8.54/8.73 intro zenon_D_pnotp. % 8.54/8.73 apply zenon_H2d2. % 8.54/8.73 rewrite <- zenon_D_pnotp. % 8.54/8.73 exact zenon_H93. % 8.54/8.73 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d3]. % 8.54/8.73 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 8.54/8.73 congruence. % 8.54/8.73 apply zenon_H2d. apply refl_equal. % 8.54/8.73 apply zenon_H2d3. apply sym_equal. exact zenon_Hbd. % 8.54/8.73 (* end of lemma zenon_L320_ *) % 8.54/8.73 assert (zenon_L321_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.54/8.73 do 0 intro. intros zenon_H1fb zenon_H2d4 zenon_H24 zenon_H29f zenon_H1d9 zenon_H2d2 zenon_H170 zenon_H1a9. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H191. zenon_intro zenon_H1fc. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_H93. zenon_intro zenon_H1c7. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_Hf4. zenon_intro zenon_H35. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H2d5 ]. % 8.54/8.73 apply (zenon_L318_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H2d6 ]. % 8.54/8.73 apply (zenon_L319_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_Hbd | zenon_intro zenon_H98 ]. % 8.54/8.73 apply (zenon_L320_); trivial. % 8.54/8.73 apply (zenon_L167_); trivial. % 8.54/8.73 (* end of lemma zenon_L321_ *) % 8.54/8.73 assert (zenon_L322_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 8.54/8.73 do 0 intro. intros zenon_H20d zenon_H24 zenon_H25. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H20d). zenon_intro zenon_H1a9. zenon_intro zenon_H20e. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H20e). zenon_intro zenon_H103. zenon_intro zenon_H177. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H1e. zenon_intro zenon_H1e. % 8.54/8.73 apply (zenon_L2_); trivial. % 8.54/8.73 (* end of lemma zenon_L322_ *) % 8.54/8.73 assert (zenon_L323_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 8.54/8.73 do 0 intro. intros zenon_H20f zenon_H24 zenon_H124. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H20f). zenon_intro zenon_H1a9. zenon_intro zenon_H210. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H210). zenon_intro zenon_H103. zenon_intro zenon_H17a. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_Hac. zenon_intro zenon_H1d. % 8.54/8.73 apply (zenon_L72_); trivial. % 8.54/8.73 (* end of lemma zenon_L323_ *) % 8.54/8.73 assert (zenon_L324_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> False). % 8.54/8.73 do 0 intro. intros zenon_Hff zenon_H103 zenon_H195. % 8.54/8.73 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 8.54/8.73 intro zenon_D_pnotp. % 8.54/8.73 apply zenon_Hff. % 8.54/8.73 rewrite <- zenon_D_pnotp. % 8.54/8.73 exact zenon_H103. % 8.54/8.73 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2d7]. % 8.54/8.73 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 8.54/8.73 congruence. % 8.54/8.73 apply zenon_H33. apply refl_equal. % 8.54/8.73 apply zenon_H2d7. apply sym_equal. exact zenon_H195. % 8.54/8.73 (* end of lemma zenon_L324_ *) % 8.54/8.73 assert (zenon_L325_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 8.54/8.73 do 0 intro. intros zenon_H2d8 zenon_H143 zenon_H12b zenon_H35 zenon_H109 zenon_H191 zenon_H197 zenon_Hff zenon_H103. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H2d9 ]. % 8.54/8.73 apply (zenon_L253_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2d9); [ zenon_intro zenon_H16b | zenon_intro zenon_H2da ]. % 8.54/8.73 apply (zenon_L106_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H3c | zenon_intro zenon_H195 ]. % 8.54/8.73 apply (zenon_L191_); trivial. % 8.54/8.73 apply (zenon_L324_); trivial. % 8.54/8.73 (* end of lemma zenon_L325_ *) % 8.54/8.73 assert (zenon_L326_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.54/8.73 do 0 intro. intros zenon_H211 zenon_H2d8 zenon_H12b zenon_H35 zenon_H109 zenon_H191 zenon_H197 zenon_Hff. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H211). zenon_intro zenon_H1a9. zenon_intro zenon_H212. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H212). zenon_intro zenon_H103. zenon_intro zenon_H17d. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H143. zenon_intro zenon_H24. % 8.54/8.73 apply (zenon_L325_); trivial. % 8.54/8.73 (* end of lemma zenon_L326_ *) % 8.54/8.73 assert (zenon_L327_ : ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 8.54/8.73 do 0 intro. intros zenon_H191 zenon_H196 zenon_Ha8. % 8.54/8.73 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H58 ]. % 8.54/8.73 cut (((e3) = (e3)) = ((e2) = (e3))). % 8.54/8.73 intro zenon_D_pnotp. % 8.54/8.73 apply zenon_Ha8. % 8.54/8.73 rewrite <- zenon_D_pnotp. % 8.54/8.73 exact zenon_Ha4. % 8.54/8.73 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.73 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 8.54/8.73 congruence. % 8.54/8.73 cut (((op (e2) (e1)) = (e2)) = ((e3) = (e2))). % 8.54/8.73 intro zenon_D_pnotp. % 8.54/8.73 apply zenon_Ha9. % 8.54/8.73 rewrite <- zenon_D_pnotp. % 8.54/8.73 exact zenon_H191. % 8.54/8.73 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.73 cut (((op (e2) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2db]. % 8.54/8.73 congruence. % 8.54/8.73 exact (zenon_H2db zenon_H196). % 8.54/8.73 apply zenon_H4b. apply refl_equal. % 8.54/8.73 apply zenon_H58. apply refl_equal. % 8.54/8.73 apply zenon_H58. apply refl_equal. % 8.54/8.73 (* end of lemma zenon_L327_ *) % 8.54/8.73 assert (zenon_L328_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.54/8.73 do 0 intro. intros zenon_H2a3 zenon_H127 zenon_H103 zenon_H35 zenon_H41 zenon_Ha8 zenon_H191 zenon_H1d3 zenon_H1a9. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2a3); [ zenon_intro zenon_H274 | zenon_intro zenon_H2b2 ]. % 8.54/8.73 apply (zenon_L315_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H2b3 ]. % 8.54/8.73 apply (zenon_L247_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H196 | zenon_intro zenon_H1b1 ]. % 8.54/8.73 apply (zenon_L327_); trivial. % 8.54/8.73 apply (zenon_L165_); trivial. % 8.54/8.73 (* end of lemma zenon_L328_ *) % 8.54/8.73 assert (zenon_L329_ : (~((op (e2) (op (e2) (e2))) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e2)) = (e1)) -> False). % 8.54/8.73 do 0 intro. intros zenon_H4c zenon_H191 zenon_H91. % 8.54/8.73 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (op (e2) (e2))) = (e2))). % 8.54/8.73 intro zenon_D_pnotp. % 8.54/8.73 apply zenon_H4c. % 8.54/8.73 rewrite <- zenon_D_pnotp. % 8.54/8.73 exact zenon_H191. % 8.54/8.73 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.73 cut (((op (e2) (e1)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2dc]. % 8.54/8.73 congruence. % 8.54/8.73 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H4e | zenon_intro zenon_H4f ]. % 8.54/8.73 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((op (e2) (e1)) = (op (e2) (op (e2) (e2))))). % 8.54/8.73 intro zenon_D_pnotp. % 8.54/8.73 apply zenon_H2dc. % 8.54/8.73 rewrite <- zenon_D_pnotp. % 8.54/8.73 exact zenon_H4e. % 8.54/8.73 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 8.54/8.73 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2dd]. % 8.54/8.73 congruence. % 8.54/8.73 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2de]. % 8.54/8.73 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.73 congruence. % 8.54/8.73 apply zenon_H4b. apply refl_equal. % 8.54/8.73 exact (zenon_H2de zenon_H91). % 8.54/8.73 apply zenon_H4f. apply refl_equal. % 8.54/8.73 apply zenon_H4f. apply refl_equal. % 8.54/8.73 apply zenon_H4b. apply refl_equal. % 8.54/8.73 (* end of lemma zenon_L329_ *) % 8.54/8.73 assert (zenon_L330_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> False). % 8.54/8.73 do 0 intro. intros zenon_H2df zenon_H67 zenon_H24 zenon_H35 zenon_H129 zenon_H191 zenon_H4c zenon_H1d9 zenon_Hf4. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.54/8.73 apply (zenon_L22_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.54/8.73 apply (zenon_L74_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.54/8.73 apply (zenon_L329_); trivial. % 8.54/8.73 apply (zenon_L319_); trivial. % 8.54/8.73 (* end of lemma zenon_L330_ *) % 8.54/8.73 assert (zenon_L331_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> False). % 8.54/8.73 do 0 intro. intros zenon_H2df zenon_H67 zenon_H24 zenon_H129 zenon_H1fb zenon_H191 zenon_H4c zenon_H1d9 zenon_Hf4. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.54/8.73 apply (zenon_L22_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.54/8.73 apply (zenon_L214_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.54/8.73 apply (zenon_L329_); trivial. % 8.54/8.73 apply (zenon_L319_); trivial. % 8.54/8.73 (* end of lemma zenon_L331_ *) % 8.54/8.73 assert (zenon_L332_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.54/8.73 do 0 intro. intros zenon_H11f zenon_H24 zenon_H153 zenon_H35 zenon_H67 zenon_H143 zenon_H12b zenon_H59 zenon_H1a9. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.54/8.73 apply (zenon_L303_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.54/8.73 apply (zenon_L263_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.54/8.73 apply (zenon_L253_); trivial. % 8.54/8.73 apply (zenon_L264_); trivial. % 8.54/8.73 (* end of lemma zenon_L332_ *) % 8.54/8.73 assert (zenon_L333_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> False). % 8.54/8.73 do 0 intro. intros zenon_H1d1 zenon_H64. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1d1). zenon_intro zenon_H1d. zenon_intro zenon_H1d2. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1d2). zenon_intro zenon_Hac. zenon_intro zenon_H1c7. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_Hf4. zenon_intro zenon_H35. % 8.54/8.73 apply (zenon_L265_); trivial. % 8.54/8.73 (* end of lemma zenon_L333_ *) % 8.54/8.73 assert (zenon_L334_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> False). % 8.54/8.73 do 0 intro. intros zenon_H1c5 zenon_H64. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1c5). zenon_intro zenon_H2a. zenon_intro zenon_H1c6. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1c6). zenon_intro zenon_H2a. zenon_intro zenon_H1c7. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_Hf4. zenon_intro zenon_H35. % 8.54/8.73 apply (zenon_L265_); trivial. % 8.54/8.73 (* end of lemma zenon_L334_ *) % 8.54/8.73 assert (zenon_L335_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> False). % 8.54/8.73 do 0 intro. intros zenon_H1fb zenon_H64. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H191. zenon_intro zenon_H1fc. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_H93. zenon_intro zenon_H1c7. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_Hf4. zenon_intro zenon_H35. % 8.54/8.73 apply (zenon_L265_); trivial. % 8.54/8.73 (* end of lemma zenon_L335_ *) % 8.54/8.73 assert (zenon_L336_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> False). % 8.54/8.73 do 0 intro. intros zenon_H11f zenon_Hc2 zenon_H211 zenon_H35 zenon_H67 zenon_H12b zenon_H59. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H211). zenon_intro zenon_H1a9. zenon_intro zenon_H212. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H212). zenon_intro zenon_H103. zenon_intro zenon_H17d. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H143. zenon_intro zenon_H24. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.54/8.73 apply (zenon_L225_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.54/8.73 apply (zenon_L263_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.54/8.73 apply (zenon_L253_); trivial. % 8.54/8.73 apply (zenon_L264_); trivial. % 8.54/8.73 (* end of lemma zenon_L336_ *) % 8.54/8.73 assert (zenon_L337_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((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)) = (op (e3) (e2)))) -> (((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (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)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.54/8.73 do 0 intro. intros zenon_H2bf zenon_H2a5 zenon_H2d4 zenon_H29f zenon_H2d2 zenon_H2e2 zenon_H1dd zenon_H164 zenon_Hf8 zenon_H2d8 zenon_H109 zenon_Hff zenon_H2a3 zenon_H127 zenon_Ha8 zenon_H2df zenon_H1d9 zenon_H153 zenon_Hb4 zenon_H36 zenon_H25 zenon_H124 zenon_H12b zenon_H67 zenon_H11f zenon_H1d7 zenon_H197 zenon_H129 zenon_H22e zenon_H31 zenon_Hab zenon_H2b zenon_H7d zenon_H192 zenon_Hc2 zenon_H1d3 zenon_H22d zenon_H191 zenon_H1f6 zenon_H170 zenon_H1a9. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c1 ]. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.54/8.73 apply (zenon_L303_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.73 apply (zenon_L308_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.73 apply (zenon_L309_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.73 apply (zenon_L115_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.73 apply (zenon_L154_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.73 apply (zenon_L120_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.73 apply (zenon_L121_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.73 apply (zenon_L196_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.73 apply (zenon_L310_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.73 apply (zenon_L197_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1a0). zenon_intro zenon_H24. zenon_intro zenon_H1a1. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1a1). zenon_intro zenon_H143. zenon_intro zenon_H1a2. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1a2). zenon_intro zenon_H93. zenon_intro zenon_H191. % 8.54/8.73 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.54/8.73 apply (zenon_L304_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.54/8.73 apply (zenon_L34_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.54/8.73 apply (zenon_L125_); trivial. % 8.54/8.73 apply (zenon_L306_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.73 apply (zenon_L199_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.73 apply (zenon_L200_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.73 apply (zenon_L134_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.73 apply (zenon_L166_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.73 apply (zenon_L168_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.73 apply (zenon_L170_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.73 apply (zenon_L311_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.73 apply (zenon_L312_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.73 apply (zenon_L141_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.73 apply (zenon_L174_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.73 apply (zenon_L143_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.73 apply (zenon_L144_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.73 apply (zenon_L203_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.73 apply (zenon_L147_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.73 apply (zenon_L204_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.73 apply (zenon_L150_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.73 apply (zenon_L206_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.73 apply (zenon_L207_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1e2). zenon_intro zenon_H35. zenon_intro zenon_H1e3. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1e3). zenon_intro zenon_Hf4. zenon_intro zenon_H1ad. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H103. zenon_intro zenon_H1a9. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H1d | zenon_intro zenon_H2e3 ]. % 8.54/8.73 apply (zenon_L72_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H6b | zenon_intro zenon_H2e4 ]. % 8.54/8.73 apply (zenon_L313_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_Hcb | zenon_intro zenon_H274 ]. % 8.54/8.73 apply (zenon_L314_); trivial. % 8.54/8.73 apply (zenon_L315_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.73 apply (zenon_L183_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.73 apply (zenon_L184_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.73 apply (zenon_L185_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.73 apply (zenon_L209_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.73 apply (zenon_L210_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.73 apply (zenon_L211_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.73 apply (zenon_L189_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.73 apply (zenon_L316_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.73 apply (zenon_L317_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.73 apply (zenon_L213_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.73 apply (zenon_L321_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.73 apply (zenon_L215_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.73 apply (zenon_L216_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.73 apply (zenon_L217_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.73 apply (zenon_L218_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.73 apply (zenon_L280_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.73 apply (zenon_L220_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.73 apply (zenon_L221_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.73 apply (zenon_L222_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.73 apply (zenon_L322_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.73 apply (zenon_L323_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.73 apply (zenon_L326_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.73 apply (zenon_L226_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.73 apply (zenon_L227_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.73 apply (zenon_L228_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.73 apply (zenon_L229_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.73 apply (zenon_L230_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.73 apply (zenon_L231_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.73 apply (zenon_L232_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.73 apply (zenon_L233_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.73 apply (zenon_L234_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.73 apply (zenon_L235_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.73 apply (zenon_L236_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.73 apply (zenon_L237_); trivial. % 8.54/8.73 apply (zenon_L238_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H41. zenon_intro zenon_H4a. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H4a). zenon_intro zenon_H154. zenon_intro zenon_H2c3. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.73 apply (zenon_L308_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.73 apply (zenon_L309_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.73 apply (zenon_L115_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.73 apply (zenon_L154_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.73 apply (zenon_L120_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.73 apply (zenon_L121_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.73 apply (zenon_L196_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.73 apply (zenon_L310_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.73 apply (zenon_L197_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.73 apply (zenon_L278_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.73 apply (zenon_L199_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.73 apply (zenon_L200_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.73 apply (zenon_L134_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.73 apply (zenon_L166_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.73 apply (zenon_L168_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.73 apply (zenon_L170_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.73 apply (zenon_L311_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.73 apply (zenon_L312_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.73 apply (zenon_L141_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.73 apply (zenon_L174_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.73 apply (zenon_L143_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.73 apply (zenon_L144_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.73 apply (zenon_L203_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.73 apply (zenon_L147_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.73 apply (zenon_L204_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.73 apply (zenon_L150_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.73 apply (zenon_L206_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.73 apply (zenon_L207_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1e2). zenon_intro zenon_H35. zenon_intro zenon_H1e3. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1e3). zenon_intro zenon_Hf4. zenon_intro zenon_H1ad. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H103. zenon_intro zenon_H1a9. % 8.54/8.73 apply (zenon_L328_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.73 apply (zenon_L183_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.73 apply (zenon_L184_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.73 apply (zenon_L185_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.73 apply (zenon_L209_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.73 apply (zenon_L210_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.73 apply (zenon_L211_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.73 apply (zenon_L189_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.73 apply (zenon_L316_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.73 apply (zenon_L317_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.73 apply (zenon_L213_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.73 apply (zenon_L279_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.73 apply (zenon_L215_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.73 apply (zenon_L216_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.73 apply (zenon_L217_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.73 apply (zenon_L218_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.73 apply (zenon_L280_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.73 apply (zenon_L220_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.73 apply (zenon_L221_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.73 apply (zenon_L222_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.73 apply (zenon_L322_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.73 apply (zenon_L323_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.73 apply (zenon_L326_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.73 apply (zenon_L226_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.73 apply (zenon_L227_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.73 apply (zenon_L228_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.73 apply (zenon_L229_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.73 apply (zenon_L230_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.73 apply (zenon_L231_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.73 apply (zenon_L232_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.73 apply (zenon_L233_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.73 apply (zenon_L234_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.73 apply (zenon_L235_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.73 apply (zenon_L236_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.73 apply (zenon_L237_); trivial. % 8.54/8.73 apply (zenon_L238_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H4c. zenon_intro zenon_H57. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.73 apply (zenon_L308_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.73 apply (zenon_L309_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.73 apply (zenon_L282_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.73 apply (zenon_L154_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.73 apply (zenon_L120_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.73 apply (zenon_L121_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.73 apply (zenon_L196_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1d1). zenon_intro zenon_H1d. zenon_intro zenon_H1d2. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1d2). zenon_intro zenon_Hac. zenon_intro zenon_H1c7. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_Hf4. zenon_intro zenon_H35. % 8.54/8.73 apply (zenon_L330_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.73 apply (zenon_L197_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.73 apply (zenon_L284_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.73 apply (zenon_L199_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.73 apply (zenon_L200_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.73 apply (zenon_L134_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.73 apply (zenon_L166_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.73 apply (zenon_L168_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.73 apply (zenon_L170_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.73 apply (zenon_L311_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.73 apply (zenon_L312_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.73 apply (zenon_L286_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.73 apply (zenon_L174_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.73 apply (zenon_L143_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.73 apply (zenon_L144_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.73 apply (zenon_L203_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1c5). zenon_intro zenon_H2a. zenon_intro zenon_H1c6. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1c6). zenon_intro zenon_H2a. zenon_intro zenon_H1c7. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_Hf4. zenon_intro zenon_H35. % 8.54/8.73 apply (zenon_L330_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.73 apply (zenon_L204_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.73 apply (zenon_L150_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.73 apply (zenon_L206_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.73 apply (zenon_L207_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1e2). zenon_intro zenon_H35. zenon_intro zenon_H1e3. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1e3). zenon_intro zenon_Hf4. zenon_intro zenon_H1ad. % 8.54/8.73 apply (zenon_L330_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.73 apply (zenon_L183_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.73 apply (zenon_L184_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.73 apply (zenon_L185_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.73 apply (zenon_L209_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.73 apply (zenon_L210_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.73 apply (zenon_L211_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.73 apply (zenon_L189_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.73 apply (zenon_L316_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.73 apply (zenon_L317_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.73 apply (zenon_L213_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H191. zenon_intro zenon_H1fc. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_H93. zenon_intro zenon_H1c7. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_Hf4. zenon_intro zenon_H35. % 8.54/8.73 apply (zenon_L331_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.73 apply (zenon_L215_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.73 apply (zenon_L216_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.73 apply (zenon_L217_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.73 apply (zenon_L218_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.73 apply (zenon_L280_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.73 apply (zenon_L220_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.73 apply (zenon_L221_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.73 apply (zenon_L222_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.73 apply (zenon_L322_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.73 apply (zenon_L323_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.73 apply (zenon_L293_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.73 apply (zenon_L226_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.73 apply (zenon_L227_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.73 apply (zenon_L228_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.73 apply (zenon_L229_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.73 apply (zenon_L230_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.73 apply (zenon_L231_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.73 apply (zenon_L232_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.73 apply (zenon_L233_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.73 apply (zenon_L234_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.73 apply (zenon_L235_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.73 apply (zenon_L236_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.73 apply (zenon_L237_); trivial. % 8.54/8.73 apply (zenon_L238_); trivial. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H59. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.73 apply (zenon_L308_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.73 apply (zenon_L309_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H17b). zenon_intro zenon_H1e. zenon_intro zenon_H17c. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H17c). zenon_intro zenon_H1e. zenon_intro zenon_H17d. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H143. zenon_intro zenon_H24. % 8.54/8.73 apply (zenon_L332_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.73 apply (zenon_L154_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.73 apply (zenon_L120_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.73 apply (zenon_L121_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.73 apply (zenon_L196_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.73 apply (zenon_L333_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.73 apply (zenon_L197_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1a0). zenon_intro zenon_H24. zenon_intro zenon_H1a1. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1a1). zenon_intro zenon_H143. zenon_intro zenon_H1a2. % 8.54/8.73 apply (zenon_L332_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.73 apply (zenon_L199_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.73 apply (zenon_L200_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.73 apply (zenon_L134_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.73 apply (zenon_L166_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.73 apply (zenon_L168_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.73 apply (zenon_L170_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.73 apply (zenon_L311_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.73 apply (zenon_L312_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1bb). zenon_intro zenon_H73. zenon_intro zenon_H1bc. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H1bc). zenon_intro zenon_H6b. zenon_intro zenon_H17d. % 8.54/8.73 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H143. zenon_intro zenon_H24. % 8.54/8.73 apply (zenon_L332_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.73 apply (zenon_L174_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.73 apply (zenon_L143_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.73 apply (zenon_L144_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.73 apply (zenon_L203_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.73 apply (zenon_L334_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.73 apply (zenon_L204_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.73 apply (zenon_L150_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.73 apply (zenon_L206_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.73 apply (zenon_L207_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.73 apply (zenon_L298_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.73 apply (zenon_L183_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.73 apply (zenon_L184_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.73 apply (zenon_L185_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.73 apply (zenon_L209_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.73 apply (zenon_L210_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.73 apply (zenon_L211_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.73 apply (zenon_L189_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.73 apply (zenon_L316_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.73 apply (zenon_L317_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.73 apply (zenon_L213_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.73 apply (zenon_L335_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.73 apply (zenon_L215_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.73 apply (zenon_L216_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.73 apply (zenon_L217_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.73 apply (zenon_L218_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.73 apply (zenon_L280_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.73 apply (zenon_L220_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.73 apply (zenon_L221_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.73 apply (zenon_L222_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.73 apply (zenon_L322_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.73 apply (zenon_L323_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.73 apply (zenon_L336_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.73 apply (zenon_L226_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.73 apply (zenon_L227_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.73 apply (zenon_L228_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.73 apply (zenon_L229_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.73 apply (zenon_L230_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.73 apply (zenon_L231_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.73 apply (zenon_L232_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.73 apply (zenon_L233_); trivial. % 8.54/8.73 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.74 apply (zenon_L234_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.74 apply (zenon_L235_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.74 apply (zenon_L236_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.74 apply (zenon_L237_); trivial. % 8.54/8.74 apply (zenon_L238_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.54/8.74 apply (zenon_L191_); trivial. % 8.54/8.74 apply (zenon_L169_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H29 | zenon_intro zenon_H2c2 ]. % 8.54/8.74 apply (zenon_L239_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2c2); [ zenon_intro zenon_H3b | zenon_intro zenon_H98 ]. % 8.54/8.74 apply (zenon_L198_); trivial. % 8.54/8.74 apply (zenon_L167_); trivial. % 8.54/8.74 (* end of lemma zenon_L337_ *) % 8.54/8.74 assert (zenon_L338_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 8.54/8.74 do 0 intro. intros zenon_H19a zenon_H143 zenon_H2a zenon_H2c9 zenon_H1a9 zenon_H170 zenon_H1f6 zenon_H22d zenon_H1d3 zenon_Hc2 zenon_H192 zenon_H7d zenon_H2b zenon_Hab zenon_H31 zenon_H22e zenon_H129 zenon_H197 zenon_H1d7 zenon_H11f zenon_H67 zenon_H12b zenon_H124 zenon_H25 zenon_H36 zenon_Hb4 zenon_H153 zenon_H1d9 zenon_H2df zenon_Ha8 zenon_H127 zenon_H2a3 zenon_Hff zenon_H109 zenon_H2d8 zenon_Hf8 zenon_H164 zenon_H1dd zenon_H2e2 zenon_H2d2 zenon_H29f zenon_H2d4 zenon_H2a5 zenon_H2bf zenon_Hb0 zenon_H66. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H165 | zenon_intro zenon_H19b ]. % 8.54/8.74 apply (zenon_L249_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H15a | zenon_intro zenon_H19c ]. % 8.54/8.74 apply (zenon_L307_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H191 | zenon_intro zenon_H196 ]. % 8.54/8.74 apply (zenon_L337_); trivial. % 8.54/8.74 apply (zenon_L258_); trivial. % 8.54/8.74 (* end of lemma zenon_L338_ *) % 8.54/8.74 assert (zenon_L339_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((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)) = (op (e3) (e2)))) -> (((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (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)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> False). % 8.54/8.74 do 0 intro. intros zenon_Hb7 zenon_H145 zenon_H74 zenon_H66 zenon_H2bf zenon_H2a5 zenon_H2d4 zenon_H29f zenon_H2d2 zenon_H2e2 zenon_H1dd zenon_H164 zenon_Hf8 zenon_H2d8 zenon_H109 zenon_Hff zenon_H2a3 zenon_H127 zenon_Ha8 zenon_H2df zenon_H1d9 zenon_H153 zenon_Hb4 zenon_H36 zenon_H25 zenon_H124 zenon_H12b zenon_H67 zenon_H11f zenon_H1d7 zenon_H197 zenon_H129 zenon_H22e zenon_H31 zenon_Hab zenon_H2b zenon_H7d zenon_H192 zenon_Hc2 zenon_H1d3 zenon_H22d zenon_H1f6 zenon_H170 zenon_H2c9 zenon_H2a zenon_H143 zenon_H19a zenon_H1a9 zenon_H295. % 8.54/8.74 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hac | zenon_intro zenon_Hb8 ]. % 8.54/8.74 apply (zenon_L248_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb9 ]. % 8.54/8.74 apply (zenon_L20_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H87 ]. % 8.54/8.74 apply (zenon_L338_); trivial. % 8.54/8.74 apply (zenon_L259_); trivial. % 8.54/8.74 (* end of lemma zenon_L339_ *) % 8.54/8.74 assert (zenon_L340_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.54/8.74 do 0 intro. intros zenon_H150 zenon_H295 zenon_H19a zenon_H2c9 zenon_H170 zenon_H1f6 zenon_H22d zenon_H1d3 zenon_Hc2 zenon_H192 zenon_H7d zenon_H2b zenon_Hab zenon_H31 zenon_H22e zenon_H129 zenon_H197 zenon_H1d7 zenon_H11f zenon_H12b zenon_H124 zenon_H25 zenon_H36 zenon_Hb4 zenon_H153 zenon_H1d9 zenon_H2df zenon_Ha8 zenon_H127 zenon_H2a3 zenon_Hff zenon_H109 zenon_H2d8 zenon_Hf8 zenon_H164 zenon_H1dd zenon_H2e2 zenon_H2d2 zenon_H29f zenon_H2d4 zenon_H2a5 zenon_H2bf zenon_H145 zenon_Hb7 zenon_H74 zenon_H2a zenon_H67 zenon_H143 zenon_Ha3 zenon_H1a9. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.54/8.74 apply (zenon_L339_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.54/8.74 apply (zenon_L20_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.54/8.74 apply (zenon_L261_); trivial. % 8.54/8.74 apply (zenon_L158_); trivial. % 8.54/8.74 (* end of lemma zenon_L340_ *) % 8.54/8.74 assert (zenon_L341_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H24 zenon_H276 zenon_Hc2. % 8.54/8.74 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H58 ]. % 8.54/8.74 cut (((e3) = (e3)) = ((e0) = (e3))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_Hc2. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_Ha4. % 8.54/8.74 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.74 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 8.54/8.74 congruence. % 8.54/8.74 cut (((op (e0) (e2)) = (e0)) = ((e3) = (e0))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_H1f8. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_H24. % 8.54/8.74 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.54/8.74 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H277]. % 8.54/8.74 congruence. % 8.54/8.74 exact (zenon_H277 zenon_H276). % 8.54/8.74 apply zenon_H3f. apply refl_equal. % 8.54/8.74 apply zenon_H58. apply refl_equal. % 8.54/8.74 apply zenon_H58. apply refl_equal. % 8.54/8.74 (* end of lemma zenon_L341_ *) % 8.54/8.74 assert (zenon_L342_ : (~((op (e2) (op (e2) (e2))) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e2)) = (e3)) -> False). % 8.54/8.74 do 0 intro. intros zenon_H4c zenon_H3c zenon_H99. % 8.54/8.74 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (op (e2) (e2))) = (e2))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_H4c. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_H3c. % 8.54/8.74 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.74 cut (((op (e2) (e3)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2e5]. % 8.54/8.74 congruence. % 8.54/8.74 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H4e | zenon_intro zenon_H4f ]. % 8.54/8.74 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((op (e2) (e3)) = (op (e2) (op (e2) (e2))))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_H2e5. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_H4e. % 8.54/8.74 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 8.54/8.74 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2e6]. % 8.54/8.74 congruence. % 8.54/8.74 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2e7]. % 8.54/8.74 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.74 congruence. % 8.54/8.74 apply zenon_H4b. apply refl_equal. % 8.54/8.74 exact (zenon_H2e7 zenon_H99). % 8.54/8.74 apply zenon_H4f. apply refl_equal. % 8.54/8.74 apply zenon_H4f. apply refl_equal. % 8.54/8.74 apply zenon_H4b. apply refl_equal. % 8.54/8.74 (* end of lemma zenon_L342_ *) % 8.54/8.74 assert (zenon_L343_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H30 zenon_Hd6 zenon_H67. % 8.54/8.74 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H68 | zenon_intro zenon_H40 ]. % 8.54/8.74 cut (((e1) = (e1)) = ((e0) = (e1))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_H67. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_H68. % 8.54/8.74 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.54/8.74 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 8.54/8.74 congruence. % 8.54/8.74 cut (((op (e0) (e3)) = (e0)) = ((e1) = (e0))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_H69. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_H30. % 8.54/8.74 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.54/8.74 cut (((op (e0) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2b4]. % 8.54/8.74 congruence. % 8.54/8.74 exact (zenon_H2b4 zenon_Hd6). % 8.54/8.74 apply zenon_H3f. apply refl_equal. % 8.54/8.74 apply zenon_H40. apply refl_equal. % 8.54/8.74 apply zenon_H40. apply refl_equal. % 8.54/8.74 (* end of lemma zenon_L343_ *) % 8.54/8.74 assert (zenon_L344_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H2a1 zenon_H295 zenon_H19a zenon_H2c9 zenon_H170 zenon_H1f6 zenon_H22d zenon_H1d3 zenon_Hc2 zenon_H192 zenon_H7d zenon_H2b zenon_Hab zenon_H31 zenon_H22e zenon_H129 zenon_H197 zenon_H1d7 zenon_H11f zenon_H12b zenon_H124 zenon_H36 zenon_Hb4 zenon_H153 zenon_H1d9 zenon_H2df zenon_Ha8 zenon_H127 zenon_H2a3 zenon_Hff zenon_H109 zenon_H2d8 zenon_Hf8 zenon_H164 zenon_H1dd zenon_H2e2 zenon_H2d2 zenon_H29f zenon_H2d4 zenon_H2a5 zenon_H2bf zenon_H145 zenon_Hb7 zenon_H6c zenon_H1a9 zenon_Ha3 zenon_H143 zenon_H2a zenon_H74 zenon_H25 zenon_H150 zenon_H30 zenon_H67. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.54/8.74 apply (zenon_L339_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.54/8.74 apply (zenon_L18_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.54/8.74 apply (zenon_L19_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.54/8.74 apply (zenon_L20_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.54/8.74 apply (zenon_L261_); trivial. % 8.54/8.74 apply (zenon_L158_); trivial. % 8.54/8.74 apply (zenon_L343_); trivial. % 8.54/8.74 (* end of lemma zenon_L344_ *) % 8.54/8.74 assert (zenon_L345_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((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)) = (op (e3) (e2)))) -> (((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (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) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((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 (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 8.54/8.74 do 0 intro. intros zenon_H285 zenon_H67 zenon_H150 zenon_H25 zenon_H74 zenon_H2a zenon_Ha3 zenon_H6c zenon_Hb7 zenon_H145 zenon_H2bf zenon_H2a5 zenon_H2d4 zenon_H29f zenon_H2d2 zenon_H2e2 zenon_H1dd zenon_H164 zenon_Hf8 zenon_H2d8 zenon_H109 zenon_H2a3 zenon_H127 zenon_Ha8 zenon_H2df zenon_H1d9 zenon_H153 zenon_Hb4 zenon_H36 zenon_H124 zenon_H12b zenon_H11f zenon_H1d7 zenon_H197 zenon_H129 zenon_H22e zenon_H31 zenon_Hab zenon_H2b zenon_H7d zenon_Hc2 zenon_H1d3 zenon_H22d zenon_H1f6 zenon_H170 zenon_H2c9 zenon_H19a zenon_H295 zenon_H2a1 zenon_H27f zenon_H1a9 zenon_H173 zenon_H137 zenon_H66 zenon_H192 zenon_H282 zenon_H3b zenon_H78 zenon_Hff zenon_H30. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H143 | zenon_intro zenon_H286 ]. % 8.54/8.74 apply (zenon_L344_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H165 | zenon_intro zenon_H287 ]. % 8.54/8.74 apply (zenon_L252_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H80 | zenon_intro zenon_H10f ]. % 8.54/8.74 apply (zenon_L40_); trivial. % 8.54/8.74 apply (zenon_L91_); trivial. % 8.54/8.74 (* end of lemma zenon_L345_ *) % 8.54/8.74 assert (zenon_L346_ : ((op (e2) (e2)) = (e2)) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H3b zenon_H99 zenon_Ha8. % 8.54/8.74 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H58 ]. % 8.54/8.74 cut (((e3) = (e3)) = ((e2) = (e3))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_Ha8. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_Ha4. % 8.54/8.74 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.74 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 8.54/8.74 congruence. % 8.54/8.74 cut (((op (e2) (e2)) = (e2)) = ((e3) = (e2))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_Ha9. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_H3b. % 8.54/8.74 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.74 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2e7]. % 8.54/8.74 congruence. % 8.54/8.74 exact (zenon_H2e7 zenon_H99). % 8.54/8.74 apply zenon_H4b. apply refl_equal. % 8.54/8.74 apply zenon_H58. apply refl_equal. % 8.54/8.74 apply zenon_H58. apply refl_equal. % 8.54/8.74 (* end of lemma zenon_L346_ *) % 8.54/8.74 assert (zenon_L347_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.54/8.74 do 0 intro. intros zenon_H2e8 zenon_Ha3 zenon_H71 zenon_H93 zenon_Ha8 zenon_H3b zenon_H170 zenon_H1a9. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2e8); [ zenon_intro zenon_H276 | zenon_intro zenon_H2e9 ]. % 8.54/8.74 apply (zenon_L245_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2e9); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H2ea ]. % 8.54/8.74 apply (zenon_L32_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_H99 | zenon_intro zenon_H98 ]. % 8.54/8.74 apply (zenon_L346_); trivial. % 8.54/8.74 apply (zenon_L167_); trivial. % 8.54/8.74 (* end of lemma zenon_L347_ *) % 8.54/8.74 assert (zenon_L348_ : (~((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 8.54/8.74 do 0 intro. intros zenon_H2eb zenon_He5. % 8.54/8.74 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.74 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2ec]. % 8.54/8.74 congruence. % 8.54/8.74 exact (zenon_H2ec zenon_He5). % 8.54/8.74 apply zenon_H58. apply refl_equal. % 8.54/8.74 (* end of lemma zenon_L348_ *) % 8.54/8.74 assert (zenon_L349_ : ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((e2) = (op (op (e3) (e3)) (e3)))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H108 zenon_He5 zenon_H111. % 8.54/8.74 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hd9 ]. % 8.54/8.74 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e2) = (op (op (e3) (e3)) (e3)))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_H111. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_Hd8. % 8.54/8.74 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 8.54/8.74 cut (((op (op (e3) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 8.54/8.74 congruence. % 8.54/8.74 cut (((op (e1) (e3)) = (e2)) = ((op (op (e3) (e3)) (e3)) = (e2))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_H112. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_H108. % 8.54/8.74 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.74 cut (((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2ed]. % 8.54/8.74 congruence. % 8.54/8.74 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hd9 ]. % 8.54/8.74 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_H2ed. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_Hd8. % 8.54/8.74 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 8.54/8.74 cut (((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2eb]. % 8.54/8.74 congruence. % 8.54/8.74 apply (zenon_L348_); trivial. % 8.54/8.74 apply zenon_Hd9. apply refl_equal. % 8.54/8.74 apply zenon_Hd9. apply refl_equal. % 8.54/8.74 apply zenon_H4b. apply refl_equal. % 8.54/8.74 apply zenon_Hd9. apply refl_equal. % 8.54/8.74 apply zenon_Hd9. apply refl_equal. % 8.54/8.74 (* end of lemma zenon_L349_ *) % 8.54/8.74 assert (zenon_L350_ : ((op (e2) (e1)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> False). % 8.54/8.74 do 0 intro. intros zenon_H165 zenon_H108 zenon_He5. % 8.54/8.74 apply (zenon_notand_s _ _ ax16); [ zenon_intro zenon_He6 | zenon_intro zenon_H2ee ]. % 8.54/8.74 apply zenon_He6. apply sym_equal. exact zenon_He5. % 8.54/8.74 apply (zenon_notand_s _ _ zenon_H2ee); [ zenon_intro zenon_H2ef | zenon_intro zenon_H111 ]. % 8.54/8.74 elim (classic ((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_Hdf | zenon_intro zenon_He0 ]. % 8.54/8.74 cut (((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3)))) = ((e0) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_H2ef. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_Hdf. % 8.54/8.74 cut (((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_He0]. % 8.54/8.74 cut (((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H2f0]. % 8.54/8.74 congruence. % 8.54/8.74 cut (((op (e2) (e1)) = (e0)) = ((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (e0))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_H2f0. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_H165. % 8.54/8.74 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.54/8.74 cut (((op (e2) (e1)) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2f1]. % 8.54/8.74 congruence. % 8.54/8.74 elim (classic ((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_Hdf | zenon_intro zenon_He0 ]. % 8.54/8.74 cut (((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3)))) = ((op (e2) (e1)) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_H2f1. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_Hdf. % 8.54/8.74 cut (((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (op (op (e3) (e3)) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_He0]. % 8.54/8.74 cut (((op (op (op (e3) (e3)) (e3)) (op (e3) (e3))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2f2]. % 8.54/8.74 congruence. % 8.54/8.74 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2ec]. % 8.54/8.74 cut (((op (op (e3) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 8.54/8.74 congruence. % 8.54/8.74 cut (((op (e1) (e3)) = (e2)) = ((op (op (e3) (e3)) (e3)) = (e2))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_H112. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_H108. % 8.54/8.74 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.74 cut (((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2ed]. % 8.54/8.74 congruence. % 8.54/8.74 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hd9 ]. % 8.54/8.74 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_H2ed. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_Hd8. % 8.54/8.74 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 8.54/8.74 cut (((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2eb]. % 8.54/8.74 congruence. % 8.54/8.74 apply (zenon_L348_); trivial. % 8.54/8.74 apply zenon_Hd9. apply refl_equal. % 8.54/8.74 apply zenon_Hd9. apply refl_equal. % 8.54/8.74 apply zenon_H4b. apply refl_equal. % 8.54/8.74 exact (zenon_H2ec zenon_He5). % 8.54/8.74 apply zenon_He0. apply refl_equal. % 8.54/8.74 apply zenon_He0. apply refl_equal. % 8.54/8.74 apply zenon_H3f. apply refl_equal. % 8.54/8.74 apply zenon_He0. apply refl_equal. % 8.54/8.74 apply zenon_He0. apply refl_equal. % 8.54/8.74 apply (zenon_L349_); trivial. % 8.54/8.74 (* end of lemma zenon_L350_ *) % 8.54/8.74 assert (zenon_L351_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> False). % 8.54/8.74 do 0 intro. intros zenon_Hf9 zenon_H1a9 zenon_Ha3 zenon_H2a zenon_Hf3 zenon_H71 zenon_H29f zenon_H165 zenon_H108. % 8.54/8.74 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hfc ]. % 8.54/8.74 apply (zenon_L158_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hfd ]. % 8.54/8.74 apply (zenon_L56_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_Hf6 | zenon_intro zenon_He5 ]. % 8.54/8.74 apply (zenon_L266_); trivial. % 8.54/8.74 apply (zenon_L350_); trivial. % 8.54/8.74 (* end of lemma zenon_L351_ *) % 8.54/8.74 assert (zenon_L352_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (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 (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H282 zenon_H192 zenon_H137 zenon_H173 zenon_H27f zenon_H2a1 zenon_H295 zenon_H19a zenon_H2c9 zenon_H1f6 zenon_H22d zenon_H1d3 zenon_Hc2 zenon_H2b zenon_Hab zenon_H31 zenon_H22e zenon_H129 zenon_H197 zenon_H1d7 zenon_H11f zenon_H12b zenon_H124 zenon_H36 zenon_Hb4 zenon_H153 zenon_H1d9 zenon_H2df zenon_H127 zenon_H2a3 zenon_H109 zenon_H2d8 zenon_Hf8 zenon_H164 zenon_H1dd zenon_H2e2 zenon_H2d2 zenon_H2d4 zenon_H2a5 zenon_H2bf zenon_H145 zenon_Hb7 zenon_H6c zenon_H1a9 zenon_Ha3 zenon_H10c zenon_Hac zenon_H7d zenon_H170 zenon_Ha8 zenon_H2e8 zenon_H285 zenon_H29f zenon_Hf3 zenon_H2a zenon_Hf9 zenon_H3b zenon_H78 zenon_Hff zenon_H74 zenon_H25 zenon_H150 zenon_H30 zenon_H67. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.54/8.74 apply (zenon_L345_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.54/8.74 apply (zenon_L18_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.54/8.74 apply (zenon_L19_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.54/8.74 apply (zenon_L20_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.54/8.74 apply (zenon_L305_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.54/8.74 apply (zenon_L46_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.54/8.74 apply (zenon_L347_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H143 | zenon_intro zenon_H286 ]. % 8.54/8.74 apply (zenon_L261_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H165 | zenon_intro zenon_H287 ]. % 8.54/8.74 apply (zenon_L351_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H80 | zenon_intro zenon_H10f ]. % 8.54/8.74 apply (zenon_L40_); trivial. % 8.54/8.74 apply (zenon_L91_); trivial. % 8.54/8.74 apply (zenon_L158_); trivial. % 8.54/8.74 apply (zenon_L343_); trivial. % 8.54/8.74 (* end of lemma zenon_L352_ *) % 8.54/8.74 assert (zenon_L353_ : (~((e0) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.54/8.74 do 0 intro. intros zenon_Hc2 zenon_H2a1 zenon_H295 zenon_H19a zenon_H2c9 zenon_H170 zenon_H1f6 zenon_H22d zenon_H1d3 zenon_H192 zenon_H7d zenon_H2b zenon_Hab zenon_H31 zenon_H22e zenon_H129 zenon_H197 zenon_H11f zenon_H12b zenon_H124 zenon_Hb4 zenon_H153 zenon_H1d9 zenon_H2df zenon_Ha8 zenon_H127 zenon_H2a3 zenon_Hff zenon_H109 zenon_H2d8 zenon_Hf8 zenon_H164 zenon_H1dd zenon_H2e2 zenon_H2d2 zenon_H29f zenon_H2d4 zenon_H2a5 zenon_H2bf zenon_H145 zenon_Hb7 zenon_H6c zenon_Ha3 zenon_H74 zenon_H25 zenon_H150 zenon_H67 zenon_H282 zenon_H137 zenon_H173 zenon_H27f zenon_H10c zenon_H2e8 zenon_H285 zenon_Hf3 zenon_Hf9 zenon_H78 zenon_H2a2 zenon_H36 zenon_H2a zenon_H3b zenon_H3a zenon_H1d7 zenon_H1a9. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.54/8.74 apply (zenon_L4_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.54/8.74 apply (zenon_L352_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.54/8.74 apply (zenon_L344_); trivial. % 8.54/8.74 apply (zenon_L133_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.54/8.74 apply (zenon_L5_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.54/8.74 apply (zenon_L6_); trivial. % 8.54/8.74 apply (zenon_L169_); trivial. % 8.54/8.74 (* end of lemma zenon_L353_ *) % 8.54/8.74 assert (zenon_L354_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.54/8.74 do 0 intro. intros zenon_H2f3 zenon_Hd0 zenon_H16d zenon_H1f zenon_H270 zenon_H2a4 zenon_H2b5 zenon_H2b8 zenon_H2c0 zenon_H169 zenon_H1dc zenon_H2a1 zenon_H295 zenon_H19a zenon_H2c9 zenon_H145 zenon_Hb7 zenon_H6c zenon_Ha3 zenon_H74 zenon_H150 zenon_H282 zenon_H137 zenon_H173 zenon_H27f zenon_H10c zenon_H2e8 zenon_H285 zenon_Hf3 zenon_Hf9 zenon_H78 zenon_H2a2 zenon_H3a zenon_H170 zenon_H1f6 zenon_H22d zenon_Hc2 zenon_H192 zenon_H7d zenon_H2b zenon_Hab zenon_H31 zenon_H22e zenon_H129 zenon_H197 zenon_H1d7 zenon_H11f zenon_H67 zenon_H12b zenon_H124 zenon_H25 zenon_H36 zenon_Hb4 zenon_H153 zenon_H1d9 zenon_H2df zenon_Ha8 zenon_H127 zenon_H2a3 zenon_Hff zenon_H109 zenon_H2d8 zenon_Hf8 zenon_H164 zenon_H1dd zenon_H2e2 zenon_H2d2 zenon_H29f zenon_H2d4 zenon_H2a5 zenon_H2bf zenon_H1d3 zenon_H1a9. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H1d | zenon_intro zenon_H2f4 ]. % 8.54/8.74 apply (zenon_L302_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2f4); [ zenon_intro zenon_H2a | zenon_intro zenon_H2f5 ]. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c1 ]. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.54/8.74 apply (zenon_L303_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.54/8.74 apply (zenon_L5_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.54/8.74 apply (zenon_L2_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.54/8.74 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.54/8.74 apply (zenon_L304_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.54/8.74 apply (zenon_L305_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.54/8.74 apply (zenon_L75_); trivial. % 8.54/8.74 apply (zenon_L306_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.54/8.74 apply (zenon_L340_); trivial. % 8.54/8.74 apply (zenon_L133_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H41. zenon_intro zenon_H4a. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H4a). zenon_intro zenon_H154. zenon_intro zenon_H2c3. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.54/8.74 apply (zenon_L2_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.54/8.74 apply (zenon_L305_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.54/8.74 apply (zenon_L46_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.54/8.74 apply (zenon_L97_); trivial. % 8.54/8.74 apply (zenon_L63_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.54/8.74 apply (zenon_L340_); trivial. % 8.54/8.74 apply (zenon_L133_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H4c. zenon_intro zenon_H57. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.54/8.74 apply (zenon_L2_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.54/8.74 apply (zenon_L305_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.54/8.74 apply (zenon_L46_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2e8); [ zenon_intro zenon_H276 | zenon_intro zenon_H2e9 ]. % 8.54/8.74 apply (zenon_L341_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2e9); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H2ea ]. % 8.54/8.74 apply (zenon_L32_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_H99 | zenon_intro zenon_H98 ]. % 8.54/8.74 apply (zenon_L342_); trivial. % 8.54/8.74 apply (zenon_L167_); trivial. % 8.54/8.74 apply (zenon_L63_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.54/8.74 apply (zenon_L100_); trivial. % 8.54/8.74 apply (zenon_L133_); trivial. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H59. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.54/8.74 apply (zenon_L2_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.54/8.74 apply (zenon_L303_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.54/8.74 apply (zenon_L105_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.54/8.74 apply (zenon_L65_); trivial. % 8.54/8.74 apply (zenon_L264_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.54/8.74 apply (zenon_L340_); trivial. % 8.54/8.74 apply (zenon_L133_); trivial. % 8.54/8.74 apply (zenon_L169_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H29 | zenon_intro zenon_H2c2 ]. % 8.54/8.74 apply (zenon_L3_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2c2); [ zenon_intro zenon_H3b | zenon_intro zenon_H98 ]. % 8.54/8.74 apply (zenon_L353_); trivial. % 8.54/8.74 apply (zenon_L167_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1b1 ]. % 8.54/8.74 apply (zenon_L337_); trivial. % 8.54/8.74 apply (zenon_L165_); trivial. % 8.54/8.74 (* end of lemma zenon_L354_ *) % 8.54/8.74 assert (zenon_L355_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H1e2 zenon_H2f3 zenon_Hd0 zenon_H16d zenon_H1f zenon_H270 zenon_H2a4 zenon_H2b5 zenon_H2b8 zenon_H2c0 zenon_H169 zenon_H1dc zenon_H2a1 zenon_H295 zenon_H19a zenon_H2c9 zenon_H145 zenon_Hb7 zenon_H6c zenon_Ha3 zenon_H74 zenon_H150 zenon_H282 zenon_H137 zenon_H173 zenon_H27f zenon_H10c zenon_H2e8 zenon_H285 zenon_Hf3 zenon_Hf9 zenon_H78 zenon_H2a2 zenon_H3a zenon_H170 zenon_H1f6 zenon_H22d zenon_Hc2 zenon_H192 zenon_H7d zenon_H2b zenon_Hab zenon_H31 zenon_H22e zenon_H129 zenon_H197 zenon_H1d7 zenon_H11f zenon_H67 zenon_H12b zenon_H124 zenon_H25 zenon_H36 zenon_Hb4 zenon_H153 zenon_H1d9 zenon_H2df zenon_Ha8 zenon_H127 zenon_H2a3 zenon_Hff zenon_H109 zenon_H2d8 zenon_Hf8 zenon_H164 zenon_H1dd zenon_H2e2 zenon_H2d2 zenon_H29f zenon_H2d4 zenon_H2a5 zenon_H2bf zenon_H1d3. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H1e2). zenon_intro zenon_H35. zenon_intro zenon_H1e3. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H1e3). zenon_intro zenon_Hf4. zenon_intro zenon_H1ad. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H103. zenon_intro zenon_H1a9. % 8.54/8.74 apply (zenon_L354_); trivial. % 8.54/8.74 (* end of lemma zenon_L355_ *) % 8.54/8.74 assert (zenon_L356_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H1e4 zenon_Ha3. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H1e4). zenon_intro zenon_H35. zenon_intro zenon_H1e5. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H1e5). zenon_intro zenon_Hf4. zenon_intro zenon_H1b0. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb3. zenon_intro zenon_H1b1. % 8.54/8.74 apply (zenon_L124_); trivial. % 8.54/8.74 (* end of lemma zenon_L356_ *) % 8.54/8.74 assert (zenon_L357_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.54/8.74 do 0 intro. intros zenon_H1e8 zenon_Heb zenon_H98. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H1e8). zenon_intro zenon_H35. zenon_intro zenon_H1e9. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H1e9). zenon_intro zenon_Hf4. zenon_intro zenon_H1b6. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_H5a. zenon_intro zenon_H5a. % 8.54/8.74 apply (zenon_L53_); trivial. % 8.54/8.74 (* end of lemma zenon_L357_ *) % 8.54/8.74 assert (zenon_L358_ : ((op (e3) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H98 zenon_Ha7 zenon_H2d2. % 8.54/8.74 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H9b | zenon_intro zenon_H9c ]. % 8.54/8.74 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e1) (e2)) = (op (e3) (e2)))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_H2d2. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_H9b. % 8.54/8.74 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 8.54/8.74 cut (((op (e3) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2f6]. % 8.54/8.74 congruence. % 8.54/8.74 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e1) (e2)))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_H2f6. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_H98. % 8.54/8.74 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2f7]. % 8.54/8.74 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 8.54/8.74 congruence. % 8.54/8.74 apply zenon_H9c. apply refl_equal. % 8.54/8.74 apply zenon_H2f7. apply sym_equal. exact zenon_Ha7. % 8.54/8.74 apply zenon_H9c. apply refl_equal. % 8.54/8.74 apply zenon_H9c. apply refl_equal. % 8.54/8.74 (* end of lemma zenon_L358_ *) % 8.54/8.74 assert (zenon_L359_ : (((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 (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H2f8 zenon_Hac zenon_Hab zenon_H35 zenon_H129 zenon_H7e zenon_H134 zenon_H98 zenon_H2d2. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_Had | zenon_intro zenon_H2f9 ]. % 8.54/8.74 apply (zenon_L33_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H29 | zenon_intro zenon_H2fa ]. % 8.54/8.74 apply (zenon_L74_); trivial. % 8.54/8.74 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H93 | zenon_intro zenon_Ha7 ]. % 8.54/8.74 apply (zenon_L86_); trivial. % 8.54/8.74 apply (zenon_L358_); trivial. % 8.54/8.74 (* end of lemma zenon_L359_ *) % 8.54/8.74 assert (zenon_L360_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H1ec zenon_H2f8 zenon_Hab zenon_H35 zenon_H129 zenon_H134 zenon_H98 zenon_H2d2. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_Hc8. zenon_intro zenon_H1ed. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H1ed). zenon_intro zenon_H7e. zenon_intro zenon_H17a. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_Hac. zenon_intro zenon_H1d. % 8.54/8.74 apply (zenon_L359_); trivial. % 8.54/8.74 (* end of lemma zenon_L360_ *) % 8.54/8.74 assert (zenon_L361_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e0) (op (e0) (e2))) = (e2))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H1f0 zenon_H118. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_Hc8. zenon_intro zenon_H1f1. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H1f1). zenon_intro zenon_H7e. zenon_intro zenon_H180. % 8.54/8.74 apply (zenon_L70_); trivial. % 8.54/8.74 (* end of lemma zenon_L361_ *) % 8.54/8.74 assert (zenon_L362_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H1f4 zenon_Hc8 zenon_H192. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H1f4). zenon_intro zenon_H191. zenon_intro zenon_H1f5. % 8.54/8.74 apply (zenon_L125_); trivial. % 8.54/8.74 (* end of lemma zenon_L362_ *) % 8.54/8.74 assert (zenon_L363_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((e1) = (e2))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H1f9 zenon_H7d. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H1f9). zenon_intro zenon_H191. zenon_intro zenon_H1fa. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H1fa). zenon_intro zenon_H93. zenon_intro zenon_H189. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H15a. zenon_intro zenon_H29. % 8.54/8.74 apply (zenon_L161_); trivial. % 8.54/8.74 (* end of lemma zenon_L363_ *) % 8.54/8.74 assert (zenon_L364_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((e1) = (e2))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H1f9 zenon_H7d. % 8.54/8.74 apply (zenon_L363_); trivial. % 8.54/8.74 (* end of lemma zenon_L364_ *) % 8.54/8.74 assert (zenon_L365_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H1fb zenon_Hc8 zenon_H192. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H191. zenon_intro zenon_H1fc. % 8.54/8.74 apply (zenon_L125_); trivial. % 8.54/8.74 (* end of lemma zenon_L365_ *) % 8.54/8.74 assert (zenon_L366_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H201 zenon_Hc8 zenon_H173. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H201). zenon_intro zenon_H3b. zenon_intro zenon_H202. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H202). zenon_intro zenon_H3b. zenon_intro zenon_H1a5. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H1a5). zenon_intro zenon_H3b. zenon_intro zenon_H3b. % 8.54/8.74 apply (zenon_L112_); trivial. % 8.54/8.74 (* end of lemma zenon_L366_ *) % 8.54/8.74 assert (zenon_L367_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H207 zenon_Hc8 zenon_H12b. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H207). zenon_intro zenon_H3c. zenon_intro zenon_H208. % 8.54/8.74 apply (zenon_L75_); trivial. % 8.54/8.74 (* end of lemma zenon_L367_ *) % 8.54/8.74 assert (zenon_L368_ : ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H3c zenon_H195 zenon_Ha8. % 8.54/8.74 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H58 ]. % 8.54/8.74 cut (((e3) = (e3)) = ((e2) = (e3))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_Ha8. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_Ha4. % 8.54/8.74 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.74 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 8.54/8.74 congruence. % 8.54/8.74 cut (((op (e2) (e3)) = (e2)) = ((e3) = (e2))). % 8.54/8.74 intro zenon_D_pnotp. % 8.54/8.74 apply zenon_Ha9. % 8.54/8.74 rewrite <- zenon_D_pnotp. % 8.54/8.74 exact zenon_H3c. % 8.54/8.74 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.74 cut (((op (e2) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2fb]. % 8.54/8.74 congruence. % 8.54/8.74 exact (zenon_H2fb zenon_H195). % 8.54/8.74 apply zenon_H4b. apply refl_equal. % 8.54/8.74 apply zenon_H58. apply refl_equal. % 8.54/8.74 apply zenon_H58. apply refl_equal. % 8.54/8.74 (* end of lemma zenon_L368_ *) % 8.54/8.74 assert (zenon_L369_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> False). % 8.54/8.74 do 0 intro. intros zenon_H209 zenon_Ha8. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H209). zenon_intro zenon_H3c. zenon_intro zenon_H20a. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H20a). zenon_intro zenon_Hbd. zenon_intro zenon_H1d6. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H195. zenon_intro zenon_H98. % 8.54/8.74 apply (zenon_L368_); trivial. % 8.54/8.74 (* end of lemma zenon_L369_ *) % 8.54/8.74 assert (zenon_L370_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.54/8.74 do 0 intro. intros zenon_H20b zenon_Heb zenon_H98. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H20b). zenon_intro zenon_H3c. zenon_intro zenon_H20c. % 8.54/8.74 apply (zenon_and_s _ _ zenon_H20c). zenon_intro zenon_Hbd. zenon_intro zenon_H1b6. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_H5a. zenon_intro zenon_H5a. % 8.54/8.75 apply (zenon_L53_); trivial. % 8.54/8.75 (* end of lemma zenon_L370_ *) % 8.54/8.75 assert (zenon_L371_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H211 zenon_H78 zenon_Hc8. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H211). zenon_intro zenon_H1a9. zenon_intro zenon_H212. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H212). zenon_intro zenon_H103. zenon_intro zenon_H17d. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H143. zenon_intro zenon_H24. % 8.54/8.75 apply (zenon_L83_); trivial. % 8.54/8.75 (* end of lemma zenon_L371_ *) % 8.54/8.75 assert (zenon_L372_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((e0) = (e3))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H213 zenon_Hc2. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H213). zenon_intro zenon_H1a9. zenon_intro zenon_H214. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H214). zenon_intro zenon_H103. zenon_intro zenon_H180. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H14e. zenon_intro zenon_H30. % 8.54/8.75 apply (zenon_L201_); trivial. % 8.54/8.75 (* end of lemma zenon_L372_ *) % 8.54/8.75 assert (zenon_L373_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((e0) = (e3))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H213 zenon_Hc2. % 8.54/8.75 apply (zenon_L372_); trivial. % 8.54/8.75 (* end of lemma zenon_L373_ *) % 8.54/8.75 assert (zenon_L374_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H215 zenon_H35 zenon_Hb4. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H215). zenon_intro zenon_H1b1. zenon_intro zenon_H216. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H216). zenon_intro zenon_Hb3. zenon_intro zenon_H183. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H183). zenon_intro zenon_H6b. zenon_intro zenon_H73. % 8.54/8.75 apply (zenon_L119_); trivial. % 8.54/8.75 (* end of lemma zenon_L374_ *) % 8.54/8.75 assert (zenon_L375_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H1d9 zenon_H1b1 zenon_H98. % 8.54/8.75 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H1d9. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H1b1. % 8.54/8.75 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1d5]. % 8.54/8.75 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2cc]. % 8.54/8.75 congruence. % 8.54/8.75 apply zenon_H2cc. apply refl_equal. % 8.54/8.75 apply zenon_H1d5. apply sym_equal. exact zenon_H98. % 8.54/8.75 (* end of lemma zenon_L375_ *) % 8.54/8.75 assert (zenon_L376_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H217 zenon_H1d9 zenon_H98. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H217). zenon_intro zenon_H1b1. zenon_intro zenon_H218. % 8.54/8.75 apply (zenon_L375_); trivial. % 8.54/8.75 (* end of lemma zenon_L376_ *) % 8.54/8.75 assert (zenon_L377_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H219 zenon_H129 zenon_H35. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H219). zenon_intro zenon_H1b1. zenon_intro zenon_H21a. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H21a). zenon_intro zenon_Hb3. zenon_intro zenon_H189. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H15a. zenon_intro zenon_H29. % 8.54/8.75 apply (zenon_L74_); trivial. % 8.54/8.75 (* end of lemma zenon_L377_ *) % 8.54/8.75 assert (zenon_L378_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H21b zenon_Ha3. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H21b). zenon_intro zenon_H1b1. zenon_intro zenon_H21c. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H21c). zenon_intro zenon_Hb3. zenon_intro zenon_H1c7. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_Hf4. zenon_intro zenon_H35. % 8.54/8.75 apply (zenon_L124_); trivial. % 8.54/8.75 (* end of lemma zenon_L378_ *) % 8.54/8.75 assert (zenon_L379_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((op (e0) (op (e0) (e2))) = (e2))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H21d zenon_H118. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H98. zenon_intro zenon_H21e. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H21e). zenon_intro zenon_H195. zenon_intro zenon_H19f. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H19f). zenon_intro zenon_H7e. zenon_intro zenon_Hc8. % 8.54/8.75 apply (zenon_L70_); trivial. % 8.54/8.75 (* end of lemma zenon_L379_ *) % 8.54/8.75 assert (zenon_L380_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H21f zenon_Hc8 zenon_H192. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H21f). zenon_intro zenon_H98. zenon_intro zenon_H220. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H220). zenon_intro zenon_H195. zenon_intro zenon_H1a2. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1a2). zenon_intro zenon_H93. zenon_intro zenon_H191. % 8.54/8.75 apply (zenon_L125_); trivial. % 8.54/8.75 (* end of lemma zenon_L380_ *) % 8.54/8.75 assert (zenon_L381_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H221 zenon_Hc8 zenon_H173. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H221). zenon_intro zenon_H98. zenon_intro zenon_H222. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H222). zenon_intro zenon_H195. zenon_intro zenon_H1a5. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1a5). zenon_intro zenon_H3b. zenon_intro zenon_H3b. % 8.54/8.75 apply (zenon_L112_); trivial. % 8.54/8.75 (* end of lemma zenon_L381_ *) % 8.54/8.75 assert (zenon_L382_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H223 zenon_Ha8. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H98. zenon_intro zenon_H224. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H224). zenon_intro zenon_H195. zenon_intro zenon_H1a8. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hbd. zenon_intro zenon_H3c. % 8.54/8.75 apply (zenon_L368_); trivial. % 8.54/8.75 (* end of lemma zenon_L382_ *) % 8.54/8.75 assert (zenon_L383_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H225 zenon_H1d7. % 8.54/8.75 apply (zenon_L235_); trivial. % 8.54/8.75 (* end of lemma zenon_L383_ *) % 8.54/8.75 assert (zenon_L384_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H2fc zenon_H1b1 zenon_H5a. % 8.54/8.75 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e3)))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H2fc. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H1b1. % 8.54/8.75 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 8.54/8.75 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2cc]. % 8.54/8.75 congruence. % 8.54/8.75 apply zenon_H2cc. apply refl_equal. % 8.54/8.75 apply zenon_Hec. apply sym_equal. exact zenon_H5a. % 8.54/8.75 (* end of lemma zenon_L384_ *) % 8.54/8.75 assert (zenon_L385_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H227 zenon_H2fc. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H227). zenon_intro zenon_H5a. zenon_intro zenon_H228. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H228). zenon_intro zenon_H5a. zenon_intro zenon_H1b0. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb3. zenon_intro zenon_H1b1. % 8.54/8.75 apply (zenon_L384_); trivial. % 8.54/8.75 (* end of lemma zenon_L385_ *) % 8.54/8.75 assert (zenon_L386_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H227 zenon_H2fc. % 8.54/8.75 apply (zenon_L385_); trivial. % 8.54/8.75 (* end of lemma zenon_L386_ *) % 8.54/8.75 assert (zenon_L387_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H229 zenon_Heb. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H229). zenon_intro zenon_H5a. zenon_intro zenon_H22a. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H22a). zenon_intro zenon_H5a. zenon_intro zenon_H1d6. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H195. zenon_intro zenon_H98. % 8.54/8.75 apply (zenon_L53_); trivial. % 8.54/8.75 (* end of lemma zenon_L387_ *) % 8.54/8.75 assert (zenon_L388_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H22b zenon_Heb zenon_H98. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H22b). zenon_intro zenon_H5a. zenon_intro zenon_H22c. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H22c). zenon_intro zenon_H5a. zenon_intro zenon_H1b6. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_H5a. zenon_intro zenon_H5a. % 8.54/8.75 apply (zenon_L53_); trivial. % 8.54/8.75 (* end of lemma zenon_L388_ *) % 8.54/8.75 assert (zenon_L389_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e1) (op (e1) (e0))) = (e0))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H1d1 zenon_H49. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1d1). zenon_intro zenon_H1d. zenon_intro zenon_H1d2. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1d2). zenon_intro zenon_Hac. zenon_intro zenon_H1c7. % 8.54/8.75 apply (zenon_L82_); trivial. % 8.54/8.75 (* end of lemma zenon_L389_ *) % 8.54/8.75 assert (zenon_L390_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H1c8 zenon_H129 zenon_H35. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_H29. zenon_intro zenon_H1c9. % 8.54/8.75 apply (zenon_L74_); trivial. % 8.54/8.75 (* end of lemma zenon_L390_ *) % 8.54/8.75 assert (zenon_L391_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H105 zenon_H10f zenon_Hd0 zenon_H35 zenon_H7e zenon_H153 zenon_Hff zenon_H195. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H30 | zenon_intro zenon_H106 ]. % 8.54/8.75 apply (zenon_L91_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H107 ]. % 8.54/8.75 apply (zenon_L246_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfe | zenon_intro zenon_H103 ]. % 8.54/8.75 apply (zenon_L96_); trivial. % 8.54/8.75 apply (zenon_L324_); trivial. % 8.54/8.75 (* end of lemma zenon_L391_ *) % 8.54/8.75 assert (zenon_L392_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H105 zenon_Hd4 zenon_He4 zenon_H31 zenon_H66 zenon_H7e zenon_H153 zenon_Hff zenon_H195. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H30 | zenon_intro zenon_H106 ]. % 8.54/8.75 apply (zenon_L66_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H107 ]. % 8.54/8.75 apply (zenon_L87_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfe | zenon_intro zenon_H103 ]. % 8.54/8.75 apply (zenon_L96_); trivial. % 8.54/8.75 apply (zenon_L324_); trivial. % 8.54/8.75 (* end of lemma zenon_L392_ *) % 8.54/8.75 assert (zenon_L393_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H11f zenon_H1d zenon_H127 zenon_H67 zenon_H35 zenon_Hd0 zenon_H105 zenon_He4 zenon_H31 zenon_H66 zenon_H7e zenon_H153 zenon_Hff zenon_H195. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.54/8.75 apply (zenon_L73_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.54/8.75 apply (zenon_L263_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.54/8.75 apply (zenon_L391_); trivial. % 8.54/8.75 apply (zenon_L392_); trivial. % 8.54/8.75 (* end of lemma zenon_L393_ *) % 8.54/8.75 assert (zenon_L394_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H30 zenon_Hfe zenon_H78. % 8.54/8.75 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H79 | zenon_intro zenon_H4b ]. % 8.54/8.75 cut (((e2) = (e2)) = ((e0) = (e2))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H78. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H79. % 8.54/8.75 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.75 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 8.54/8.75 congruence. % 8.54/8.75 cut (((op (e0) (e3)) = (e0)) = ((e2) = (e0))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H7a. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H30. % 8.54/8.75 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.54/8.75 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H13d]. % 8.54/8.75 congruence. % 8.54/8.75 exact (zenon_H13d zenon_Hfe). % 8.54/8.75 apply zenon_H3f. apply refl_equal. % 8.54/8.75 apply zenon_H4b. apply refl_equal. % 8.54/8.75 apply zenon_H4b. apply refl_equal. % 8.54/8.75 (* end of lemma zenon_L394_ *) % 8.54/8.75 assert (zenon_L395_ : ((op (e2) (e1)) = (e1)) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H15a zenon_H196 zenon_Ha3. % 8.54/8.75 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H58 ]. % 8.54/8.75 cut (((e3) = (e3)) = ((e1) = (e3))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_Ha3. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_Ha4. % 8.54/8.75 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.75 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 8.54/8.75 congruence. % 8.54/8.75 cut (((op (e2) (e1)) = (e1)) = ((e3) = (e1))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_Ha5. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H15a. % 8.54/8.75 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.54/8.75 cut (((op (e2) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2db]. % 8.54/8.75 congruence. % 8.54/8.75 exact (zenon_H2db zenon_H196). % 8.54/8.75 apply zenon_H40. apply refl_equal. % 8.54/8.75 apply zenon_H58. apply refl_equal. % 8.54/8.75 apply zenon_H58. apply refl_equal. % 8.54/8.75 (* end of lemma zenon_L395_ *) % 8.54/8.75 assert (zenon_L396_ : (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (e2)) = (e1)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H7d zenon_H3b zenon_H91. % 8.54/8.75 cut (((op (e2) (e2)) = (e2)) = ((e1) = (e2))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H7d. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H3b. % 8.54/8.75 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.75 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2de]. % 8.54/8.75 congruence. % 8.54/8.75 exact (zenon_H2de zenon_H91). % 8.54/8.75 apply zenon_H4b. apply refl_equal. % 8.54/8.75 (* end of lemma zenon_L396_ *) % 8.54/8.75 assert (zenon_L397_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H134 zenon_H24 zenon_Had. % 8.54/8.75 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H134. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H24. % 8.54/8.75 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 8.54/8.75 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 8.54/8.75 congruence. % 8.54/8.75 apply zenon_H27. apply refl_equal. % 8.54/8.75 apply zenon_Hae. apply sym_equal. exact zenon_Had. % 8.54/8.75 (* end of lemma zenon_L397_ *) % 8.54/8.75 assert (zenon_L398_ : ((op (e3) (e2)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 8.54/8.75 do 0 intro. intros zenon_Hbd zenon_H7e zenon_H29f. % 8.54/8.75 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H9b | zenon_intro zenon_H9c ]. % 8.54/8.75 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e0) (e2)) = (op (e3) (e2)))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H29f. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H9b. % 8.54/8.75 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 8.54/8.75 cut (((op (e3) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2fd]. % 8.54/8.75 congruence. % 8.54/8.75 cut (((op (e3) (e2)) = (e2)) = ((op (e3) (e2)) = (op (e0) (e2)))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H2fd. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_Hbd. % 8.54/8.75 cut (((e2) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2fe]. % 8.54/8.75 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 8.54/8.75 congruence. % 8.54/8.75 apply zenon_H9c. apply refl_equal. % 8.54/8.75 apply zenon_H2fe. apply sym_equal. exact zenon_H7e. % 8.54/8.75 apply zenon_H9c. apply refl_equal. % 8.54/8.75 apply zenon_H9c. apply refl_equal. % 8.54/8.75 (* end of lemma zenon_L398_ *) % 8.54/8.75 assert (zenon_L399_ : ((op (e3) (e2)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H98 zenon_H276 zenon_H29f. % 8.54/8.75 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H9b | zenon_intro zenon_H9c ]. % 8.54/8.75 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e0) (e2)) = (op (e3) (e2)))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H29f. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H9b. % 8.54/8.75 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 8.54/8.75 cut (((op (e3) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2fd]. % 8.54/8.75 congruence. % 8.54/8.75 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e0) (e2)))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H2fd. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H98. % 8.54/8.75 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2ff]. % 8.54/8.75 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 8.54/8.75 congruence. % 8.54/8.75 apply zenon_H9c. apply refl_equal. % 8.54/8.75 apply zenon_H2ff. apply sym_equal. exact zenon_H276. % 8.54/8.75 apply zenon_H9c. apply refl_equal. % 8.54/8.75 apply zenon_H9c. apply refl_equal. % 8.54/8.75 (* end of lemma zenon_L399_ *) % 8.54/8.75 assert (zenon_L400_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H300 zenon_Had zenon_H134 zenon_H25 zenon_H66 zenon_Hbd zenon_H98 zenon_H29f. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H24 | zenon_intro zenon_H301 ]. % 8.54/8.75 apply (zenon_L397_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H71 | zenon_intro zenon_H302 ]. % 8.54/8.75 apply (zenon_L19_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H7e | zenon_intro zenon_H276 ]. % 8.54/8.75 apply (zenon_L398_); trivial. % 8.54/8.75 apply (zenon_L399_); trivial. % 8.54/8.75 (* end of lemma zenon_L400_ *) % 8.54/8.75 assert (zenon_L401_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 8.54/8.75 do 0 intro. intros zenon_Hbf zenon_H195 zenon_Hff zenon_H153 zenon_H35 zenon_Hd0 zenon_H10f zenon_H105 zenon_H154 zenon_H91 zenon_H7d zenon_H300 zenon_Had zenon_H134 zenon_H25 zenon_H66 zenon_H98 zenon_H29f. % 8.54/8.75 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H7e | zenon_intro zenon_Hc0 ]. % 8.54/8.75 apply (zenon_L391_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H93 | zenon_intro zenon_Hc1 ]. % 8.54/8.75 apply (zenon_L97_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H3b | zenon_intro zenon_Hbd ]. % 8.54/8.75 apply (zenon_L396_); trivial. % 8.54/8.75 apply (zenon_L400_); trivial. % 8.54/8.75 (* end of lemma zenon_L401_ *) % 8.54/8.75 assert (zenon_L402_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H303 zenon_Hc8 zenon_Ha3 zenon_H196 zenon_H29f zenon_H98 zenon_H66 zenon_H25 zenon_H134 zenon_Had zenon_H300 zenon_H7d zenon_H154 zenon_H105 zenon_H10f zenon_Hd0 zenon_H153 zenon_Hff zenon_H195 zenon_Hbf zenon_H109 zenon_H35. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.54/8.75 apply (zenon_L44_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.54/8.75 apply (zenon_L395_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.54/8.75 apply (zenon_L401_); trivial. % 8.54/8.75 apply (zenon_L106_); trivial. % 8.54/8.75 (* end of lemma zenon_L402_ *) % 8.54/8.75 assert (zenon_L403_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H90 zenon_H24 zenon_H80. % 8.54/8.75 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e2) (e2)))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H90. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H24. % 8.54/8.75 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 8.54/8.75 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 8.54/8.75 congruence. % 8.54/8.75 apply zenon_H27. apply refl_equal. % 8.54/8.75 apply zenon_H89. apply sym_equal. exact zenon_H80. % 8.54/8.75 (* end of lemma zenon_L403_ *) % 8.54/8.75 assert (zenon_L404_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H150 zenon_H25 zenon_H71 zenon_Hb4 zenon_H35 zenon_Hc8 zenon_H7d zenon_H14e zenon_H67. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.54/8.75 apply (zenon_L19_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.54/8.75 apply (zenon_L119_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.54/8.75 apply (zenon_L44_); trivial. % 8.54/8.75 apply (zenon_L94_); trivial. % 8.54/8.75 (* end of lemma zenon_L404_ *) % 8.54/8.75 assert (zenon_L405_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 8.54/8.75 do 0 intro. intros zenon_Hc5 zenon_H124 zenon_H1d zenon_H109 zenon_Hbf zenon_H154 zenon_H134 zenon_H66 zenon_H196 zenon_Ha3 zenon_H303 zenon_H29f zenon_H98 zenon_H105 zenon_H10f zenon_Hd0 zenon_H35 zenon_H153 zenon_Hff zenon_H195 zenon_H150 zenon_H25 zenon_Hb4 zenon_Hc8 zenon_H7d zenon_H67 zenon_H90 zenon_H300 zenon_H170 zenon_H14e. % 8.54/8.75 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_H24 | zenon_intro zenon_Hc6 ]. % 8.54/8.75 apply (zenon_L72_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Had | zenon_intro zenon_Hc7 ]. % 8.54/8.75 apply (zenon_L402_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H80 | zenon_intro zenon_Hc3 ]. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H24 | zenon_intro zenon_H301 ]. % 8.54/8.75 apply (zenon_L403_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H71 | zenon_intro zenon_H302 ]. % 8.54/8.75 apply (zenon_L404_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H7e | zenon_intro zenon_H276 ]. % 8.54/8.75 apply (zenon_L391_); trivial. % 8.54/8.75 apply (zenon_L399_); trivial. % 8.54/8.75 apply (zenon_L111_); trivial. % 8.54/8.75 (* end of lemma zenon_L405_ *) % 8.54/8.75 assert (zenon_L406_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H1f0 zenon_H127 zenon_H1d. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_Hc8. zenon_intro zenon_H1f1. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1f1). zenon_intro zenon_H7e. zenon_intro zenon_H180. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H14e. zenon_intro zenon_H30. % 8.54/8.75 apply (zenon_L73_); trivial. % 8.54/8.75 (* end of lemma zenon_L406_ *) % 8.54/8.75 assert (zenon_L407_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H205 zenon_H2f3 zenon_Hd0 zenon_H16d zenon_H1f zenon_H270 zenon_H2a4 zenon_H2b5 zenon_H2b8 zenon_H2c0 zenon_H169 zenon_H1dc zenon_H2a1 zenon_H295 zenon_H19a zenon_H2c9 zenon_H145 zenon_Hb7 zenon_H6c zenon_Ha3 zenon_H74 zenon_H150 zenon_H282 zenon_H137 zenon_H173 zenon_H27f zenon_H10c zenon_H2e8 zenon_H285 zenon_Hf3 zenon_Hf9 zenon_H78 zenon_H2a2 zenon_H3a zenon_H170 zenon_H1f6 zenon_H22d zenon_Hc2 zenon_H192 zenon_H7d zenon_H2b zenon_Hab zenon_H31 zenon_H22e zenon_H129 zenon_H197 zenon_H1d7 zenon_H11f zenon_H67 zenon_H12b zenon_H124 zenon_H25 zenon_H36 zenon_Hb4 zenon_H153 zenon_H1d9 zenon_H2df zenon_Ha8 zenon_H127 zenon_H2a3 zenon_Hff zenon_H109 zenon_H2d8 zenon_Hf8 zenon_H164 zenon_H1dd zenon_H2e2 zenon_H2d2 zenon_H29f zenon_H2d4 zenon_H2a5 zenon_H2bf zenon_H1d3. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H3c. zenon_intro zenon_H206. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_Hbd. zenon_intro zenon_H1ad. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H103. zenon_intro zenon_H1a9. % 8.54/8.75 apply (zenon_L354_); trivial. % 8.54/8.75 (* end of lemma zenon_L407_ *) % 8.54/8.75 assert (zenon_L408_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H217 zenon_H35 zenon_H36. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H217). zenon_intro zenon_H1b1. zenon_intro zenon_H218. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H218). zenon_intro zenon_Hb3. zenon_intro zenon_H186. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H186). zenon_intro zenon_H2a. zenon_intro zenon_H2a. % 8.54/8.75 apply (zenon_L5_); trivial. % 8.54/8.75 (* end of lemma zenon_L408_ *) % 8.54/8.75 assert (zenon_L409_ : (~((op (e2) (op (e2) (e3))) = (e3))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H57 zenon_H195. % 8.54/8.75 cut (((op (e2) (e3)) = (e3)) = ((op (e2) (op (e2) (e3))) = (e3))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H57. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H195. % 8.54/8.75 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.75 cut (((op (e2) (e3)) = (op (e2) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H306]. % 8.54/8.75 congruence. % 8.54/8.75 elim (classic ((op (e2) (op (e2) (e3))) = (op (e2) (op (e2) (e3))))); [ zenon_intro zenon_H307 | zenon_intro zenon_H308 ]. % 8.54/8.75 cut (((op (e2) (op (e2) (e3))) = (op (e2) (op (e2) (e3)))) = ((op (e2) (e3)) = (op (e2) (op (e2) (e3))))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H306. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H307. % 8.54/8.75 cut (((op (e2) (op (e2) (e3))) = (op (e2) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H308]. % 8.54/8.75 cut (((op (e2) (op (e2) (e3))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H309]. % 8.54/8.75 congruence. % 8.54/8.75 cut (((op (e2) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2fb]. % 8.54/8.75 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.75 congruence. % 8.54/8.75 apply zenon_H4b. apply refl_equal. % 8.54/8.75 exact (zenon_H2fb zenon_H195). % 8.54/8.75 apply zenon_H308. apply refl_equal. % 8.54/8.75 apply zenon_H308. apply refl_equal. % 8.54/8.75 apply zenon_H58. apply refl_equal. % 8.54/8.75 (* end of lemma zenon_L409_ *) % 8.54/8.75 assert (zenon_L410_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H1b2 zenon_H57. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_H30. zenon_intro zenon_H1b3. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1b3). zenon_intro zenon_H14e. zenon_intro zenon_H1d6. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H195. zenon_intro zenon_H98. % 8.54/8.75 apply (zenon_L409_); trivial. % 8.54/8.75 (* end of lemma zenon_L410_ *) % 8.54/8.75 assert (zenon_L411_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H1c8 zenon_H56. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_H29. zenon_intro zenon_H1c9. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1c9). zenon_intro zenon_H15a. zenon_intro zenon_H19f. % 8.54/8.75 apply (zenon_L99_); trivial. % 8.54/8.75 (* end of lemma zenon_L411_ *) % 8.54/8.75 assert (zenon_L412_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H1e6 zenon_H57. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H35. zenon_intro zenon_H1e7. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_Hf4. zenon_intro zenon_H1d6. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H195. zenon_intro zenon_H98. % 8.54/8.75 apply (zenon_L409_); trivial. % 8.54/8.75 (* end of lemma zenon_L412_ *) % 8.54/8.75 assert (zenon_L413_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H20f zenon_H2bf zenon_H1dc zenon_H1dd zenon_H169 zenon_H2c0 zenon_H1d9 zenon_H2b8 zenon_H2b5 zenon_H109 zenon_H197 zenon_H22e zenon_H31 zenon_Hab zenon_H2b zenon_H7d zenon_H129 zenon_H1f6 zenon_H124 zenon_H1d7 zenon_H3a zenon_H2a5 zenon_H2a4 zenon_H270 zenon_Hc2 zenon_H1d3 zenon_Hb7 zenon_H78 zenon_H192 zenon_H145 zenon_H285 zenon_H295 zenon_H2a3 zenon_Hb4 zenon_H25 zenon_H150 zenon_H1f zenon_H2a2 zenon_H2a1 zenon_H282 zenon_H12b zenon_H137 zenon_H173 zenon_H27f zenon_H127 zenon_H11f zenon_H67 zenon_H16d zenon_H29f zenon_Ha3 zenon_Hf9 zenon_Hd0 zenon_H22d zenon_H170. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H20f). zenon_intro zenon_H1a9. zenon_intro zenon_H210. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H210). zenon_intro zenon_H103. zenon_intro zenon_H17a. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_Hac. zenon_intro zenon_H1d. % 8.54/8.75 apply (zenon_L302_); trivial. % 8.54/8.75 (* end of lemma zenon_L413_ *) % 8.54/8.75 assert (zenon_L414_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H219 zenon_H56. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H219). zenon_intro zenon_H1b1. zenon_intro zenon_H21a. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H21a). zenon_intro zenon_Hb3. zenon_intro zenon_H189. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H15a. zenon_intro zenon_H29. % 8.54/8.75 apply (zenon_L99_); trivial. % 8.54/8.75 (* end of lemma zenon_L414_ *) % 8.54/8.75 assert (zenon_L415_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H21d zenon_H57. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H98. zenon_intro zenon_H21e. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H21e). zenon_intro zenon_H195. zenon_intro zenon_H19f. % 8.54/8.75 apply (zenon_L409_); trivial. % 8.54/8.75 (* end of lemma zenon_L415_ *) % 8.54/8.75 assert (zenon_L416_ : (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e3) (e0)) = (e0)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H62 zenon_H14e. % 8.54/8.75 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (op (e3) (e0))) = (e0))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H62. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H14e. % 8.54/8.75 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.54/8.75 cut (((op (e3) (e0)) = (op (e3) (op (e3) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H30a]. % 8.54/8.75 congruence. % 8.54/8.75 elim (classic ((op (e3) (op (e3) (e0))) = (op (e3) (op (e3) (e0))))); [ zenon_intro zenon_H30b | zenon_intro zenon_H30c ]. % 8.54/8.75 cut (((op (e3) (op (e3) (e0))) = (op (e3) (op (e3) (e0)))) = ((op (e3) (e0)) = (op (e3) (op (e3) (e0))))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H30a. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H30b. % 8.54/8.75 cut (((op (e3) (op (e3) (e0))) = (op (e3) (op (e3) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H30c]. % 8.54/8.75 cut (((op (e3) (op (e3) (e0))) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H30d]. % 8.54/8.75 congruence. % 8.54/8.75 cut (((op (e3) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 8.54/8.75 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.75 congruence. % 8.54/8.75 apply zenon_H58. apply refl_equal. % 8.54/8.75 exact (zenon_H1aa zenon_H14e). % 8.54/8.75 apply zenon_H30c. apply refl_equal. % 8.54/8.75 apply zenon_H30c. apply refl_equal. % 8.54/8.75 apply zenon_H3f. apply refl_equal. % 8.54/8.75 (* end of lemma zenon_L416_ *) % 8.54/8.75 assert (zenon_L417_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H17e zenon_H62. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H17e). zenon_intro zenon_H1e. zenon_intro zenon_H17f. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H17f). zenon_intro zenon_H1e. zenon_intro zenon_H180. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H14e. zenon_intro zenon_H30. % 8.54/8.75 apply (zenon_L416_); trivial. % 8.54/8.75 (* end of lemma zenon_L417_ *) % 8.54/8.75 assert (zenon_L418_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H1b2 zenon_H62. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_H30. zenon_intro zenon_H1b3. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1b3). zenon_intro zenon_H14e. zenon_intro zenon_H1d6. % 8.54/8.75 apply (zenon_L416_); trivial. % 8.54/8.75 (* end of lemma zenon_L418_ *) % 8.54/8.75 assert (zenon_L419_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H1bd zenon_H62. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1bd). zenon_intro zenon_H73. zenon_intro zenon_H1be. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_H6b. zenon_intro zenon_H180. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H14e. zenon_intro zenon_H30. % 8.54/8.75 apply (zenon_L416_); trivial. % 8.54/8.75 (* end of lemma zenon_L419_ *) % 8.54/8.75 assert (zenon_L420_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H2a2 zenon_H1f zenon_H1d zenon_H2d2 zenon_H98 zenon_H134 zenon_H7e zenon_H129 zenon_H35 zenon_Hab zenon_H2f8 zenon_Hc8 zenon_H78 zenon_H62. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.54/8.75 apply (zenon_L1_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.54/8.75 apply (zenon_L359_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.54/8.75 apply (zenon_L83_); trivial. % 8.54/8.75 apply (zenon_L416_); trivial. % 8.54/8.75 (* end of lemma zenon_L420_ *) % 8.54/8.75 assert (zenon_L421_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H1e6 zenon_H64. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H35. zenon_intro zenon_H1e7. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_Hf4. zenon_intro zenon_H1d6. % 8.54/8.75 apply (zenon_L265_); trivial. % 8.54/8.75 (* end of lemma zenon_L421_ *) % 8.54/8.75 assert (zenon_L422_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H1f0 zenon_H62. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_Hc8. zenon_intro zenon_H1f1. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H1f1). zenon_intro zenon_H7e. zenon_intro zenon_H180. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H14e. zenon_intro zenon_H30. % 8.54/8.75 apply (zenon_L416_); trivial. % 8.54/8.75 (* end of lemma zenon_L422_ *) % 8.54/8.75 assert (zenon_L423_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H207 zenon_H65. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H207). zenon_intro zenon_H3c. zenon_intro zenon_H208. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H208). zenon_intro zenon_Hbd. zenon_intro zenon_H1b0. % 8.54/8.75 apply (zenon_L295_); trivial. % 8.54/8.75 (* end of lemma zenon_L423_ *) % 8.54/8.75 assert (zenon_L424_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H11f zenon_Hc2 zenon_H103 zenon_H35 zenon_H67 zenon_H143 zenon_H12b zenon_H59 zenon_H1a9. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.54/8.75 apply (zenon_L201_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.54/8.75 apply (zenon_L263_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.54/8.75 apply (zenon_L253_); trivial. % 8.54/8.75 apply (zenon_L264_); trivial. % 8.54/8.75 (* end of lemma zenon_L424_ *) % 8.54/8.75 assert (zenon_L425_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> False). % 8.54/8.75 do 0 intro. intros zenon_H211 zenon_H11f zenon_Hc2 zenon_H35 zenon_H67 zenon_H12b zenon_H59. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H211). zenon_intro zenon_H1a9. zenon_intro zenon_H212. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H212). zenon_intro zenon_H103. zenon_intro zenon_H17d. % 8.54/8.75 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H143. zenon_intro zenon_H24. % 8.54/8.75 apply (zenon_L424_); trivial. % 8.54/8.75 (* end of lemma zenon_L425_ *) % 8.54/8.75 assert (zenon_L426_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 8.54/8.75 do 0 intro. intros zenon_Hac zenon_H87 zenon_Hc2. % 8.54/8.75 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H58 ]. % 8.54/8.75 cut (((e3) = (e3)) = ((e0) = (e3))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_Hc2. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_Ha4. % 8.54/8.75 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.75 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 8.54/8.75 congruence. % 8.54/8.75 cut (((op (e1) (e0)) = (e0)) = ((e3) = (e0))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H1f8. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_Hac. % 8.54/8.75 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.54/8.75 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H30e]. % 8.54/8.75 congruence. % 8.54/8.75 exact (zenon_H30e zenon_H87). % 8.54/8.75 apply zenon_H3f. apply refl_equal. % 8.54/8.75 apply zenon_H58. apply refl_equal. % 8.54/8.75 apply zenon_H58. apply refl_equal. % 8.54/8.75 (* end of lemma zenon_L426_ *) % 8.54/8.75 assert (zenon_L427_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 8.54/8.75 do 0 intro. intros zenon_Hba zenon_Hc2 zenon_Hac zenon_Ha3 zenon_H2a zenon_Ha8 zenon_H93 zenon_H5a zenon_H16d. % 8.54/8.75 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.54/8.75 apply (zenon_L426_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.54/8.75 apply (zenon_L31_); trivial. % 8.54/8.75 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.54/8.75 apply (zenon_L32_); trivial. % 8.54/8.75 apply (zenon_L109_); trivial. % 8.54/8.75 (* end of lemma zenon_L427_ *) % 8.54/8.75 assert (zenon_L428_ : ((op (e0) (e1)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 8.54/8.75 do 0 intro. intros zenon_Hcb zenon_H274 zenon_Ha8. % 8.54/8.75 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H58 ]. % 8.54/8.75 cut (((e3) = (e3)) = ((e2) = (e3))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_Ha8. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_Ha4. % 8.54/8.75 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.75 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 8.54/8.75 congruence. % 8.54/8.75 cut (((op (e0) (e1)) = (e2)) = ((e3) = (e2))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_Ha9. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_Hcb. % 8.54/8.75 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.75 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H275]. % 8.54/8.75 congruence. % 8.54/8.75 exact (zenon_H275 zenon_H274). % 8.54/8.75 apply zenon_H4b. apply refl_equal. % 8.54/8.75 apply zenon_H58. apply refl_equal. % 8.54/8.75 apply zenon_H58. apply refl_equal. % 8.54/8.75 (* end of lemma zenon_L428_ *) % 8.54/8.75 assert (zenon_L429_ : (~((op (op (e2) (e2)) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e1)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H30f zenon_H91. % 8.54/8.75 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.75 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2de]. % 8.54/8.75 congruence. % 8.54/8.75 exact (zenon_H2de zenon_H91). % 8.54/8.75 apply zenon_H4b. apply refl_equal. % 8.54/8.75 (* end of lemma zenon_L429_ *) % 8.54/8.75 assert (zenon_L430_ : ((op (e1) (e2)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> (~((e3) = (op (op (e2) (e2)) (e2)))) -> False). % 8.54/8.75 do 0 intro. intros zenon_Ha7 zenon_H91 zenon_H310. % 8.54/8.75 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H83 | zenon_intro zenon_H84 ]. % 8.54/8.75 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e3) = (op (op (e2) (e2)) (e2)))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H310. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H83. % 8.54/8.75 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 8.54/8.75 cut (((op (op (e2) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H311]. % 8.54/8.75 congruence. % 8.54/8.75 cut (((op (e1) (e2)) = (e3)) = ((op (op (e2) (e2)) (e2)) = (e3))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H311. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_Ha7. % 8.54/8.75 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.75 cut (((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H312]. % 8.54/8.75 congruence. % 8.54/8.75 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H83 | zenon_intro zenon_H84 ]. % 8.54/8.75 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H312. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H83. % 8.54/8.75 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 8.54/8.75 cut (((op (op (e2) (e2)) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H30f]. % 8.54/8.75 congruence. % 8.54/8.75 apply (zenon_L429_); trivial. % 8.54/8.75 apply zenon_H84. apply refl_equal. % 8.54/8.75 apply zenon_H84. apply refl_equal. % 8.54/8.75 apply zenon_H58. apply refl_equal. % 8.54/8.75 apply zenon_H84. apply refl_equal. % 8.54/8.75 apply zenon_H84. apply refl_equal. % 8.54/8.75 (* end of lemma zenon_L430_ *) % 8.54/8.75 assert (zenon_L431_ : ((op (e3) (e1)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> False). % 8.54/8.75 do 0 intro. intros zenon_H1df zenon_Ha7 zenon_H91. % 8.54/8.75 apply (zenon_notand_s _ _ ax14); [ zenon_intro zenon_H92 | zenon_intro zenon_H313 ]. % 8.54/8.75 apply zenon_H92. apply sym_equal. exact zenon_H91. % 8.54/8.75 apply (zenon_notand_s _ _ zenon_H313); [ zenon_intro zenon_H314 | zenon_intro zenon_H310 ]. % 8.54/8.75 elim (classic ((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ]. % 8.54/8.75 cut (((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2)))) = ((e0) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H314. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H8b. % 8.54/8.75 cut (((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 8.54/8.75 cut (((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H315]. % 8.54/8.75 congruence. % 8.54/8.75 cut (((op (e3) (e1)) = (e0)) = ((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (e0))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H315. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H1df. % 8.54/8.75 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.54/8.75 cut (((op (e3) (e1)) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H316]. % 8.54/8.75 congruence. % 8.54/8.75 elim (classic ((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ]. % 8.54/8.75 cut (((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2)))) = ((op (e3) (e1)) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H316. % 8.54/8.75 rewrite <- zenon_D_pnotp. % 8.54/8.75 exact zenon_H8b. % 8.54/8.75 cut (((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 8.54/8.75 cut (((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H317]. % 8.54/8.75 congruence. % 8.54/8.75 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2de]. % 8.54/8.75 cut (((op (op (e2) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H311]. % 8.54/8.75 congruence. % 8.54/8.75 cut (((op (e1) (e2)) = (e3)) = ((op (op (e2) (e2)) (e2)) = (e3))). % 8.54/8.75 intro zenon_D_pnotp. % 8.54/8.75 apply zenon_H311. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_Ha7. % 8.54/8.76 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.76 cut (((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H312]. % 8.54/8.76 congruence. % 8.54/8.76 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H83 | zenon_intro zenon_H84 ]. % 8.54/8.76 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_H312. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_H83. % 8.54/8.76 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 8.54/8.76 cut (((op (op (e2) (e2)) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H30f]. % 8.54/8.76 congruence. % 8.54/8.76 apply (zenon_L429_); trivial. % 8.54/8.76 apply zenon_H84. apply refl_equal. % 8.54/8.76 apply zenon_H84. apply refl_equal. % 8.54/8.76 apply zenon_H58. apply refl_equal. % 8.54/8.76 exact (zenon_H2de zenon_H91). % 8.54/8.76 apply zenon_H8c. apply refl_equal. % 8.54/8.76 apply zenon_H8c. apply refl_equal. % 8.54/8.76 apply zenon_H3f. apply refl_equal. % 8.54/8.76 apply zenon_H8c. apply refl_equal. % 8.54/8.76 apply zenon_H8c. apply refl_equal. % 8.54/8.76 apply (zenon_L430_); trivial. % 8.54/8.76 (* end of lemma zenon_L431_ *) % 8.54/8.76 assert (zenon_L432_ : ((op (e3) (e1)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 8.54/8.76 do 0 intro. intros zenon_H1b1 zenon_H196 zenon_H169. % 8.54/8.76 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H2cb | zenon_intro zenon_H2cc ]. % 8.54/8.76 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e2) (e1)) = (op (e3) (e1)))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_H169. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_H2cb. % 8.54/8.76 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2cc]. % 8.54/8.76 cut (((op (e3) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H318]. % 8.54/8.76 congruence. % 8.54/8.76 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e2) (e1)))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_H318. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_H1b1. % 8.54/8.76 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 8.54/8.76 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2cc]. % 8.54/8.76 congruence. % 8.54/8.76 apply zenon_H2cc. apply refl_equal. % 8.54/8.76 apply zenon_H199. apply sym_equal. exact zenon_H196. % 8.54/8.76 apply zenon_H2cc. apply refl_equal. % 8.54/8.76 apply zenon_H2cc. apply refl_equal. % 8.54/8.76 (* end of lemma zenon_L432_ *) % 8.54/8.76 assert (zenon_L433_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 8.54/8.76 do 0 intro. intros zenon_Hbf zenon_H78 zenon_H24 zenon_Ha8 zenon_H173 zenon_Hc8 zenon_H1dc zenon_H91 zenon_Ha7 zenon_H2a zenon_Hf3 zenon_H1d9 zenon_H196 zenon_H169. % 8.54/8.76 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H7e | zenon_intro zenon_Hc0 ]. % 8.54/8.76 apply (zenon_L128_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H93 | zenon_intro zenon_Hc1 ]. % 8.54/8.76 apply (zenon_L32_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H3b | zenon_intro zenon_Hbd ]. % 8.54/8.76 apply (zenon_L112_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H1df | zenon_intro zenon_H1de ]. % 8.54/8.76 apply (zenon_L431_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H1e1 ]. % 8.54/8.76 apply (zenon_L56_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H1b1 ]. % 8.54/8.76 apply (zenon_L180_); trivial. % 8.54/8.76 apply (zenon_L432_); trivial. % 8.54/8.76 (* end of lemma zenon_L433_ *) % 8.54/8.76 assert (zenon_L434_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 8.54/8.76 do 0 intro. intros zenon_H105 zenon_Hd1 zenon_H16b zenon_Hff zenon_H108 zenon_Hd0 zenon_H5a zenon_He4. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H30 | zenon_intro zenon_H106 ]. % 8.54/8.76 apply (zenon_L47_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H107 ]. % 8.54/8.76 apply (zenon_L107_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfe | zenon_intro zenon_H103 ]. % 8.54/8.76 apply (zenon_L88_); trivial. % 8.54/8.76 apply (zenon_L89_); trivial. % 8.54/8.76 (* end of lemma zenon_L434_ *) % 8.54/8.76 assert (zenon_L435_ : (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H27f zenon_Hc8 zenon_Hf1. % 8.54/8.76 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e3) (e0)))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_H27f. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_Hc8. % 8.54/8.76 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H319]. % 8.54/8.76 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 8.54/8.76 congruence. % 8.54/8.76 apply zenon_H139. apply refl_equal. % 8.54/8.76 apply zenon_H319. apply sym_equal. exact zenon_Hf1. % 8.54/8.76 (* end of lemma zenon_L435_ *) % 8.54/8.76 assert (zenon_L436_ : ((op (e1) (e0)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (~((e3) = (op (op (e0) (e0)) (e0)))) -> False). % 8.54/8.76 do 0 intro. intros zenon_H87 zenon_H66 zenon_H31a. % 8.54/8.76 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H28a | zenon_intro zenon_H28b ]. % 8.54/8.76 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e3) = (op (op (e0) (e0)) (e0)))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_H31a. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_H28a. % 8.54/8.76 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H28b]. % 8.54/8.76 cut (((op (op (e0) (e0)) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H31b]. % 8.54/8.76 congruence. % 8.54/8.76 cut (((op (e1) (e0)) = (e3)) = ((op (op (e0) (e0)) (e0)) = (e3))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_H31b. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_H87. % 8.54/8.76 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.76 cut (((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H28d]. % 8.54/8.76 congruence. % 8.54/8.76 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H28a | zenon_intro zenon_H28b ]. % 8.54/8.76 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_H28d. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_H28a. % 8.54/8.76 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H28b]. % 8.54/8.76 cut (((op (op (e0) (e0)) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H288]. % 8.54/8.76 congruence. % 8.54/8.76 apply (zenon_L256_); trivial. % 8.54/8.76 apply zenon_H28b. apply refl_equal. % 8.54/8.76 apply zenon_H28b. apply refl_equal. % 8.54/8.76 apply zenon_H58. apply refl_equal. % 8.54/8.76 apply zenon_H28b. apply refl_equal. % 8.54/8.76 apply zenon_H28b. apply refl_equal. % 8.54/8.76 (* end of lemma zenon_L436_ *) % 8.54/8.76 assert (zenon_L437_ : ((op (e3) (e1)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H1d8 zenon_H87 zenon_H66. % 8.54/8.76 apply (zenon_notand_s _ _ ax12); [ zenon_intro zenon_H72 | zenon_intro zenon_H31c ]. % 8.54/8.76 apply zenon_H72. apply sym_equal. exact zenon_H66. % 8.54/8.76 apply (zenon_notand_s _ _ zenon_H31c); [ zenon_intro zenon_H31d | zenon_intro zenon_H31a ]. % 8.54/8.76 elim (classic ((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H290 | zenon_intro zenon_H291 ]. % 8.54/8.76 cut (((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0)))) = ((e2) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_H31d. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_H290. % 8.54/8.76 cut (((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H291]. % 8.54/8.76 cut (((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H31e]. % 8.54/8.76 congruence. % 8.54/8.76 cut (((op (e3) (e1)) = (e2)) = ((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (e2))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_H31e. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_H1d8. % 8.54/8.76 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.76 cut (((op (e3) (e1)) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H31f]. % 8.54/8.76 congruence. % 8.54/8.76 elim (classic ((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H290 | zenon_intro zenon_H291 ]. % 8.54/8.76 cut (((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0)))) = ((op (e3) (e1)) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_H31f. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_H290. % 8.54/8.76 cut (((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H291]. % 8.54/8.76 cut (((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H320]. % 8.54/8.76 congruence. % 8.54/8.76 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 8.54/8.76 cut (((op (op (e0) (e0)) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H31b]. % 8.54/8.76 congruence. % 8.54/8.76 cut (((op (e1) (e0)) = (e3)) = ((op (op (e0) (e0)) (e0)) = (e3))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_H31b. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_H87. % 8.54/8.76 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.76 cut (((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H28d]. % 8.54/8.76 congruence. % 8.54/8.76 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H28a | zenon_intro zenon_H28b ]. % 8.54/8.76 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_H28d. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_H28a. % 8.54/8.76 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H28b]. % 8.54/8.76 cut (((op (op (e0) (e0)) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H288]. % 8.54/8.76 congruence. % 8.54/8.76 apply (zenon_L256_); trivial. % 8.54/8.76 apply zenon_H28b. apply refl_equal. % 8.54/8.76 apply zenon_H28b. apply refl_equal. % 8.54/8.76 apply zenon_H58. apply refl_equal. % 8.54/8.76 exact (zenon_H6a zenon_H66). % 8.54/8.76 apply zenon_H291. apply refl_equal. % 8.54/8.76 apply zenon_H291. apply refl_equal. % 8.54/8.76 apply zenon_H4b. apply refl_equal. % 8.54/8.76 apply zenon_H291. apply refl_equal. % 8.54/8.76 apply zenon_H291. apply refl_equal. % 8.54/8.76 apply (zenon_L436_); trivial. % 8.54/8.76 (* end of lemma zenon_L437_ *) % 8.54/8.76 assert (zenon_L438_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 8.54/8.76 do 0 intro. intros zenon_Hba zenon_H66 zenon_H1d8 zenon_Ha3 zenon_H2a zenon_Ha8 zenon_H93 zenon_H5a zenon_H16d. % 8.54/8.76 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.54/8.76 apply (zenon_L437_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.54/8.76 apply (zenon_L31_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.54/8.76 apply (zenon_L32_); trivial. % 8.54/8.76 apply (zenon_L109_); trivial. % 8.54/8.76 (* end of lemma zenon_L438_ *) % 8.54/8.76 assert (zenon_L439_ : (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> False). % 8.54/8.76 do 0 intro. intros zenon_Ha8 zenon_H5a zenon_He8. % 8.54/8.76 cut (((op (e3) (e3)) = (e3)) = ((e2) = (e3))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_Ha8. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_H5a. % 8.54/8.76 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.76 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H321]. % 8.54/8.76 congruence. % 8.54/8.76 exact (zenon_H321 zenon_He8). % 8.54/8.76 apply zenon_H58. apply refl_equal. % 8.54/8.76 (* end of lemma zenon_L439_ *) % 8.54/8.76 assert (zenon_L440_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H322 zenon_Hc8 zenon_H27f zenon_H16d zenon_H2a zenon_Ha3 zenon_H66 zenon_Hba zenon_H93 zenon_H2d2 zenon_Ha8 zenon_H5a. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H323 ]. % 8.54/8.76 apply (zenon_L435_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H324 ]. % 8.54/8.76 apply (zenon_L438_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_Hbd | zenon_intro zenon_He8 ]. % 8.54/8.76 apply (zenon_L320_); trivial. % 8.54/8.76 apply (zenon_L439_); trivial. % 8.54/8.76 (* end of lemma zenon_L440_ *) % 8.54/8.76 assert (zenon_L441_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H10c zenon_H145 zenon_H7d zenon_H5a zenon_Ha8 zenon_H2d2 zenon_Hba zenon_H66 zenon_Ha3 zenon_H2a zenon_H16d zenon_H27f zenon_Hc8 zenon_H322 zenon_Hd0 zenon_Hfe. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.54/8.76 apply (zenon_L84_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.54/8.76 apply (zenon_L46_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.54/8.76 apply (zenon_L440_); trivial. % 8.54/8.76 apply (zenon_L88_); trivial. % 8.54/8.76 (* end of lemma zenon_L441_ *) % 8.54/8.76 assert (zenon_L442_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H17e zenon_H153 zenon_H24. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H17e). zenon_intro zenon_H1e. zenon_intro zenon_H17f. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H17f). zenon_intro zenon_H1e. zenon_intro zenon_H180. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H14e. zenon_intro zenon_H30. % 8.54/8.76 apply (zenon_L303_); trivial. % 8.54/8.76 (* end of lemma zenon_L442_ *) % 8.54/8.76 assert (zenon_L443_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H1b2 zenon_H1d9 zenon_H1b1. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_H30. zenon_intro zenon_H1b3. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1b3). zenon_intro zenon_H14e. zenon_intro zenon_H1d6. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H195. zenon_intro zenon_H98. % 8.54/8.76 apply (zenon_L375_); trivial. % 8.54/8.76 (* end of lemma zenon_L443_ *) % 8.54/8.76 assert (zenon_L444_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H1b4 zenon_H2fc zenon_H1b1. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1b4). zenon_intro zenon_H30. zenon_intro zenon_H1b5. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1b5). zenon_intro zenon_H14e. zenon_intro zenon_H1b6. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_H5a. zenon_intro zenon_H5a. % 8.54/8.76 apply (zenon_L384_); trivial. % 8.54/8.76 (* end of lemma zenon_L444_ *) % 8.54/8.76 assert (zenon_L445_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H1bd zenon_H153 zenon_H24. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1bd). zenon_intro zenon_H73. zenon_intro zenon_H1be. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_H6b. zenon_intro zenon_H180. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H14e. zenon_intro zenon_H30. % 8.54/8.76 apply (zenon_L303_); trivial. % 8.54/8.76 (* end of lemma zenon_L445_ *) % 8.54/8.76 assert (zenon_L446_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H1e6 zenon_H1d9 zenon_H1b1. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H35. zenon_intro zenon_H1e7. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_Hf4. zenon_intro zenon_H1d6. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H195. zenon_intro zenon_H98. % 8.54/8.76 apply (zenon_L375_); trivial. % 8.54/8.76 (* end of lemma zenon_L446_ *) % 8.54/8.76 assert (zenon_L447_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H1e8 zenon_H2fc zenon_H1b1. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1e8). zenon_intro zenon_H35. zenon_intro zenon_H1e9. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1e9). zenon_intro zenon_Hf4. zenon_intro zenon_H1b6. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_H5a. zenon_intro zenon_H5a. % 8.54/8.76 apply (zenon_L384_); trivial. % 8.54/8.76 (* end of lemma zenon_L447_ *) % 8.54/8.76 assert (zenon_L448_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 8.54/8.76 do 0 intro. intros zenon_H1ea zenon_H24 zenon_H25. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1ea). zenon_intro zenon_Hc8. zenon_intro zenon_H1eb. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1eb). zenon_intro zenon_H7e. zenon_intro zenon_H177. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H1e. zenon_intro zenon_H1e. % 8.54/8.76 apply (zenon_L2_); trivial. % 8.54/8.76 (* end of lemma zenon_L448_ *) % 8.54/8.76 assert (zenon_L449_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 8.54/8.76 do 0 intro. intros zenon_H1ec zenon_H24 zenon_H124. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_Hc8. zenon_intro zenon_H1ed. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1ed). zenon_intro zenon_H7e. zenon_intro zenon_H17a. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_Hac. zenon_intro zenon_H1d. % 8.54/8.76 apply (zenon_L72_); trivial. % 8.54/8.76 (* end of lemma zenon_L449_ *) % 8.54/8.76 assert (zenon_L450_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H1f0 zenon_H153 zenon_H24. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_Hc8. zenon_intro zenon_H1f1. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1f1). zenon_intro zenon_H7e. zenon_intro zenon_H180. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H14e. zenon_intro zenon_H30. % 8.54/8.76 apply (zenon_L303_); trivial. % 8.54/8.76 (* end of lemma zenon_L450_ *) % 8.54/8.76 assert (zenon_L451_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H209 zenon_H1d9 zenon_H1b1. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H209). zenon_intro zenon_H3c. zenon_intro zenon_H20a. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H20a). zenon_intro zenon_Hbd. zenon_intro zenon_H1d6. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H195. zenon_intro zenon_H98. % 8.54/8.76 apply (zenon_L375_); trivial. % 8.54/8.76 (* end of lemma zenon_L451_ *) % 8.54/8.76 assert (zenon_L452_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H20b zenon_H2fc zenon_H1b1. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H20b). zenon_intro zenon_H3c. zenon_intro zenon_H20c. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H20c). zenon_intro zenon_Hbd. zenon_intro zenon_H1b6. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_H5a. zenon_intro zenon_H5a. % 8.54/8.76 apply (zenon_L384_); trivial. % 8.54/8.76 (* end of lemma zenon_L452_ *) % 8.54/8.76 assert (zenon_L453_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H21d zenon_H1d9 zenon_H1b1. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H98. zenon_intro zenon_H21e. % 8.54/8.76 apply (zenon_L375_); trivial. % 8.54/8.76 (* end of lemma zenon_L453_ *) % 8.54/8.76 assert (zenon_L454_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H229 zenon_H1d9 zenon_H1b1. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H229). zenon_intro zenon_H5a. zenon_intro zenon_H22a. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H22a). zenon_intro zenon_H5a. zenon_intro zenon_H1d6. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H195. zenon_intro zenon_H98. % 8.54/8.76 apply (zenon_L375_); trivial. % 8.54/8.76 (* end of lemma zenon_L454_ *) % 8.54/8.76 assert (zenon_L455_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H22b zenon_H2fc zenon_H1b1. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H22b). zenon_intro zenon_H5a. zenon_intro zenon_H22c. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H22c). zenon_intro zenon_H5a. zenon_intro zenon_H1b6. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_H5a. zenon_intro zenon_H5a. % 8.54/8.76 apply (zenon_L384_); trivial. % 8.54/8.76 (* end of lemma zenon_L455_ *) % 8.54/8.76 assert (zenon_L456_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> False). % 8.54/8.76 do 0 intro. intros zenon_H1c8 zenon_H24 zenon_H78. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_H29. zenon_intro zenon_H1c9. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1c9). zenon_intro zenon_H15a. zenon_intro zenon_H19f. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H19f). zenon_intro zenon_H7e. zenon_intro zenon_Hc8. % 8.54/8.76 apply (zenon_L128_); trivial. % 8.54/8.76 (* end of lemma zenon_L456_ *) % 8.54/8.76 assert (zenon_L457_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H205 zenon_H1d3 zenon_H1b1. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H3c. zenon_intro zenon_H206. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_Hbd. zenon_intro zenon_H1ad. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H103. zenon_intro zenon_H1a9. % 8.54/8.76 apply (zenon_L165_); trivial. % 8.54/8.76 (* end of lemma zenon_L457_ *) % 8.54/8.76 assert (zenon_L458_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.54/8.76 do 0 intro. intros zenon_H2df zenon_H67 zenon_H24 zenon_H129 zenon_H1fb zenon_H4c zenon_H1d9. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H191. zenon_intro zenon_H1fc. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_H93. zenon_intro zenon_H1c7. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_Hf4. zenon_intro zenon_H35. % 8.54/8.76 apply (zenon_L331_); trivial. % 8.54/8.76 (* end of lemma zenon_L458_ *) % 8.54/8.76 assert (zenon_L459_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> False). % 8.54/8.76 do 0 intro. intros zenon_H1ae zenon_H62. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_H30. zenon_intro zenon_H1af. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_H14e. zenon_intro zenon_H1b0. % 8.54/8.76 apply (zenon_L416_); trivial. % 8.54/8.76 (* end of lemma zenon_L459_ *) % 8.54/8.76 assert (zenon_L460_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H187 zenon_H127 zenon_H30. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H187). zenon_intro zenon_H1d. zenon_intro zenon_H188. % 8.54/8.76 apply (zenon_L73_); trivial. % 8.54/8.76 (* end of lemma zenon_L460_ *) % 8.54/8.76 assert (zenon_L461_ : (~((op (e0) (op (e0) (e0))) = (e0))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H12e zenon_H30 zenon_H26f. % 8.54/8.76 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (op (e0) (e0))) = (e0))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_H12e. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_H30. % 8.54/8.76 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.54/8.76 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H325]. % 8.54/8.76 congruence. % 8.54/8.76 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H130 | zenon_intro zenon_H131 ]. % 8.54/8.76 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e3)) = (op (e0) (op (e0) (e0))))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_H325. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_H130. % 8.54/8.76 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 8.54/8.76 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H326]. % 8.54/8.76 congruence. % 8.54/8.76 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H327]. % 8.54/8.76 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.54/8.76 congruence. % 8.54/8.76 apply zenon_H3f. apply refl_equal. % 8.54/8.76 exact (zenon_H327 zenon_H26f). % 8.54/8.76 apply zenon_H131. apply refl_equal. % 8.54/8.76 apply zenon_H131. apply refl_equal. % 8.54/8.76 apply zenon_H3f. apply refl_equal. % 8.54/8.76 (* end of lemma zenon_L461_ *) % 8.54/8.76 assert (zenon_L462_ : ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> False). % 8.54/8.76 do 0 intro. intros zenon_Hc8 zenon_H27e zenon_Ha8. % 8.54/8.76 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H58 ]. % 8.54/8.76 cut (((e3) = (e3)) = ((e2) = (e3))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_Ha8. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_Ha4. % 8.54/8.76 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.76 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 8.54/8.76 congruence. % 8.54/8.76 cut (((op (e2) (e0)) = (e2)) = ((e3) = (e2))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_Ha9. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_Hc8. % 8.54/8.76 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.76 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H328]. % 8.54/8.76 congruence. % 8.54/8.76 exact (zenon_H328 zenon_H27e). % 8.54/8.76 apply zenon_H4b. apply refl_equal. % 8.54/8.76 apply zenon_H58. apply refl_equal. % 8.54/8.76 apply zenon_H58. apply refl_equal. % 8.54/8.76 (* end of lemma zenon_L462_ *) % 8.54/8.76 assert (zenon_L463_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 8.54/8.76 do 0 intro. intros zenon_H1bd zenon_H29 zenon_Hab. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1bd). zenon_intro zenon_H73. zenon_intro zenon_H1be. % 8.54/8.76 apply (zenon_L93_); trivial. % 8.54/8.76 (* end of lemma zenon_L463_ *) % 8.54/8.76 assert (zenon_L464_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> False). % 8.54/8.76 do 0 intro. intros zenon_H1ea zenon_H30 zenon_H31. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1ea). zenon_intro zenon_Hc8. zenon_intro zenon_H1eb. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1eb). zenon_intro zenon_H7e. zenon_intro zenon_H177. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H1e. zenon_intro zenon_H1e. % 8.54/8.76 apply (zenon_L4_); trivial. % 8.54/8.76 (* end of lemma zenon_L464_ *) % 8.54/8.76 assert (zenon_L465_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H1ec zenon_H127 zenon_H30. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_Hc8. zenon_intro zenon_H1ed. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1ed). zenon_intro zenon_H7e. zenon_intro zenon_H17a. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_Hac. zenon_intro zenon_H1d. % 8.54/8.76 apply (zenon_L73_); trivial. % 8.54/8.76 (* end of lemma zenon_L465_ *) % 8.54/8.76 assert (zenon_L466_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H2d2 zenon_H29 zenon_Hf6. % 8.54/8.76 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_H2d2. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_H29. % 8.54/8.76 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2a0]. % 8.54/8.76 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 8.54/8.76 congruence. % 8.54/8.76 apply zenon_H2d. apply refl_equal. % 8.54/8.76 apply zenon_H2a0. apply sym_equal. exact zenon_Hf6. % 8.54/8.76 (* end of lemma zenon_L466_ *) % 8.54/8.76 assert (zenon_L467_ : (((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 (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H2d4 zenon_H14e zenon_H170 zenon_H29 zenon_H2d2 zenon_H29f zenon_H7e zenon_H1d9 zenon_H1b1. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H2d5 ]. % 8.54/8.76 apply (zenon_L111_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H2d6 ]. % 8.54/8.76 apply (zenon_L466_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_Hbd | zenon_intro zenon_H98 ]. % 8.54/8.76 apply (zenon_L398_); trivial. % 8.54/8.76 apply (zenon_L375_); trivial. % 8.54/8.76 (* end of lemma zenon_L467_ *) % 8.54/8.76 assert (zenon_L468_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H1f0 zenon_H2d4 zenon_H170 zenon_H29 zenon_H2d2 zenon_H29f zenon_H1d9 zenon_H1b1. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_Hc8. zenon_intro zenon_H1f1. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1f1). zenon_intro zenon_H7e. zenon_intro zenon_H180. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H14e. zenon_intro zenon_H30. % 8.54/8.76 apply (zenon_L467_); trivial. % 8.54/8.76 (* end of lemma zenon_L468_ *) % 8.54/8.76 assert (zenon_L469_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 8.54/8.76 do 0 intro. intros zenon_H215 zenon_H29 zenon_Hab. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H215). zenon_intro zenon_H1b1. zenon_intro zenon_H216. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H216). zenon_intro zenon_Hb3. zenon_intro zenon_H183. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H183). zenon_intro zenon_H6b. zenon_intro zenon_H73. % 8.54/8.76 apply (zenon_L93_); trivial. % 8.54/8.76 (* end of lemma zenon_L469_ *) % 8.54/8.76 assert (zenon_L470_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 8.54/8.76 do 0 intro. intros zenon_H217 zenon_H29 zenon_H2b. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H217). zenon_intro zenon_H1b1. zenon_intro zenon_H218. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H218). zenon_intro zenon_Hb3. zenon_intro zenon_H186. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H186). zenon_intro zenon_H2a. zenon_intro zenon_H2a. % 8.54/8.76 apply (zenon_L3_); trivial. % 8.54/8.76 (* end of lemma zenon_L470_ *) % 8.54/8.76 assert (zenon_L471_ : ((op (e1) (e3)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 8.54/8.76 do 0 intro. intros zenon_H108 zenon_Hb3 zenon_Ha8. % 8.54/8.76 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H58 ]. % 8.54/8.76 cut (((e3) = (e3)) = ((e2) = (e3))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_Ha8. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_Ha4. % 8.54/8.76 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.76 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 8.54/8.76 congruence. % 8.54/8.76 cut (((op (e1) (e3)) = (e2)) = ((e3) = (e2))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_Ha9. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_H108. % 8.54/8.76 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.76 cut (((op (e1) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 8.54/8.76 congruence. % 8.54/8.76 exact (zenon_H190 zenon_Hb3). % 8.54/8.76 apply zenon_H4b. apply refl_equal. % 8.54/8.76 apply zenon_H58. apply refl_equal. % 8.54/8.76 apply zenon_H58. apply refl_equal. % 8.54/8.76 (* end of lemma zenon_L471_ *) % 8.54/8.76 assert (zenon_L472_ : (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H197 zenon_H15a zenon_H16b. % 8.54/8.76 cut (((op (e2) (e1)) = (e1)) = ((op (e2) (e1)) = (op (e2) (e3)))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_H197. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_H15a. % 8.54/8.76 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 8.54/8.76 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 8.54/8.76 congruence. % 8.54/8.76 apply zenon_H16a. apply refl_equal. % 8.54/8.76 apply zenon_H16c. apply sym_equal. exact zenon_H16b. % 8.54/8.76 (* end of lemma zenon_L472_ *) % 8.54/8.76 assert (zenon_L473_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H109 zenon_Hb3 zenon_H195. % 8.54/8.76 cut (((op (e1) (e3)) = (e3)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_H109. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_Hb3. % 8.54/8.76 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2d7]. % 8.54/8.76 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 8.54/8.76 congruence. % 8.54/8.76 apply zenon_H38. apply refl_equal. % 8.54/8.76 apply zenon_H2d7. apply sym_equal. exact zenon_H195. % 8.54/8.76 (* end of lemma zenon_L473_ *) % 8.54/8.76 assert (zenon_L474_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H2d8 zenon_H30 zenon_Hff zenon_H15a zenon_H197 zenon_He8 zenon_He7 zenon_H109 zenon_Hb3. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H2d9 ]. % 8.54/8.76 apply (zenon_L91_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2d9); [ zenon_intro zenon_H16b | zenon_intro zenon_H2da ]. % 8.54/8.76 apply (zenon_L472_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H3c | zenon_intro zenon_H195 ]. % 8.54/8.76 apply (zenon_L52_); trivial. % 8.54/8.76 apply (zenon_L473_); trivial. % 8.54/8.76 (* end of lemma zenon_L474_ *) % 8.54/8.76 assert (zenon_L475_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 8.54/8.76 do 0 intro. intros zenon_H219 zenon_H329 zenon_H78 zenon_Ha8 zenon_H12b zenon_Hc8 zenon_H2d8 zenon_H30 zenon_Hff zenon_H197 zenon_He7 zenon_H109. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H219). zenon_intro zenon_H1b1. zenon_intro zenon_H21a. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H21a). zenon_intro zenon_Hb3. zenon_intro zenon_H189. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H15a. zenon_intro zenon_H29. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hfe | zenon_intro zenon_H32a ]. % 8.54/8.76 apply (zenon_L394_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H108 | zenon_intro zenon_H32b ]. % 8.54/8.76 apply (zenon_L471_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H3c | zenon_intro zenon_He8 ]. % 8.54/8.76 apply (zenon_L75_); trivial. % 8.54/8.76 apply (zenon_L474_); trivial. % 8.54/8.76 (* end of lemma zenon_L475_ *) % 8.54/8.76 assert (zenon_L476_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 8.54/8.76 do 0 intro. intros zenon_H10c zenon_H145 zenon_Hc8 zenon_H41 zenon_H7d zenon_H29 zenon_Hb3 zenon_Ha8. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.54/8.76 apply (zenon_L84_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.54/8.76 apply (zenon_L85_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.54/8.76 apply (zenon_L161_); trivial. % 8.54/8.76 apply (zenon_L471_); trivial. % 8.54/8.76 (* end of lemma zenon_L476_ *) % 8.54/8.76 assert (zenon_L477_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 8.54/8.76 do 0 intro. intros zenon_Hc5 zenon_H30 zenon_H153 zenon_H29 zenon_H67 zenon_Hc8 zenon_H4c zenon_H170 zenon_H14e. % 8.54/8.76 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_H24 | zenon_intro zenon_Hc6 ]. % 8.54/8.76 apply (zenon_L303_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Had | zenon_intro zenon_Hc7 ]. % 8.54/8.76 apply (zenon_L110_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H80 | zenon_intro zenon_Hc3 ]. % 8.54/8.76 apply (zenon_L102_); trivial. % 8.54/8.76 apply (zenon_L111_); trivial. % 8.54/8.76 (* end of lemma zenon_L477_ *) % 8.54/8.76 assert (zenon_L478_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 8.54/8.76 do 0 intro. intros zenon_Hc5 zenon_H78 zenon_H7e zenon_H29 zenon_H67 zenon_Hc8 zenon_H4c zenon_H170 zenon_H14e. % 8.54/8.76 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_H24 | zenon_intro zenon_Hc6 ]. % 8.54/8.76 apply (zenon_L128_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Had | zenon_intro zenon_Hc7 ]. % 8.54/8.76 apply (zenon_L110_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H80 | zenon_intro zenon_Hc3 ]. % 8.54/8.76 apply (zenon_L102_); trivial. % 8.54/8.76 apply (zenon_L111_); trivial. % 8.54/8.76 (* end of lemma zenon_L478_ *) % 8.54/8.76 assert (zenon_L479_ : (~((op (e3) (op (e3) (e3))) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H59 zenon_H1b1 zenon_He5. % 8.54/8.76 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (op (e3) (e3))) = (e3))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_H59. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_H1b1. % 8.54/8.76 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.76 cut (((op (e3) (e1)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H32c]. % 8.54/8.76 congruence. % 8.54/8.76 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 8.54/8.76 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((op (e3) (e1)) = (op (e3) (op (e3) (e3))))). % 8.54/8.76 intro zenon_D_pnotp. % 8.54/8.76 apply zenon_H32c. % 8.54/8.76 rewrite <- zenon_D_pnotp. % 8.54/8.76 exact zenon_H5c. % 8.54/8.76 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 8.54/8.76 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H32d]. % 8.54/8.76 congruence. % 8.54/8.76 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2ec]. % 8.54/8.76 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.76 congruence. % 8.54/8.76 apply zenon_H58. apply refl_equal. % 8.54/8.76 exact (zenon_H2ec zenon_He5). % 8.54/8.76 apply zenon_H5d. apply refl_equal. % 8.54/8.76 apply zenon_H5d. apply refl_equal. % 8.54/8.76 apply zenon_H58. apply refl_equal. % 8.54/8.76 (* end of lemma zenon_L479_ *) % 8.54/8.76 assert (zenon_L480_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H2b8 zenon_H67 zenon_H30 zenon_H29 zenon_H129 zenon_H15a zenon_H197 zenon_H59 zenon_H1b1. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H2b9 ]. % 8.54/8.76 apply (zenon_L343_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_H35 | zenon_intro zenon_H2ba ]. % 8.54/8.76 apply (zenon_L74_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H16b | zenon_intro zenon_He5 ]. % 8.54/8.76 apply (zenon_L472_); trivial. % 8.54/8.76 apply (zenon_L479_); trivial. % 8.54/8.76 (* end of lemma zenon_L480_ *) % 8.54/8.76 assert (zenon_L481_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H2b8 zenon_H67 zenon_H30 zenon_Ha3 zenon_Hb3 zenon_H15a zenon_H197 zenon_H59 zenon_H1b1. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H2b9 ]. % 8.54/8.76 apply (zenon_L343_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_H35 | zenon_intro zenon_H2ba ]. % 8.54/8.76 apply (zenon_L124_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H16b | zenon_intro zenon_He5 ]. % 8.54/8.76 apply (zenon_L472_); trivial. % 8.54/8.76 apply (zenon_L479_); trivial. % 8.54/8.76 (* end of lemma zenon_L481_ *) % 8.54/8.76 assert (zenon_L482_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> False). % 8.54/8.76 do 0 intro. intros zenon_H219 zenon_H2b8 zenon_H67 zenon_H30 zenon_Ha3 zenon_H197 zenon_H59. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H219). zenon_intro zenon_H1b1. zenon_intro zenon_H21a. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H21a). zenon_intro zenon_Hb3. zenon_intro zenon_H189. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H15a. zenon_intro zenon_H29. % 8.54/8.76 apply (zenon_L481_); trivial. % 8.54/8.76 (* end of lemma zenon_L482_ *) % 8.54/8.76 assert (zenon_L483_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H22d zenon_H1d9 zenon_H1d7 zenon_Ha8 zenon_H173 zenon_H192 zenon_Ha3 zenon_H2b8 zenon_H67 zenon_H197 zenon_H2b zenon_Hab zenon_Hc2 zenon_H1f6 zenon_H7d zenon_H78 zenon_H127 zenon_H31 zenon_H25 zenon_H22e zenon_H153 zenon_H170 zenon_Hc5 zenon_H3a zenon_H2a2 zenon_H29f zenon_H2d2 zenon_H2d4 zenon_H145 zenon_H10c zenon_Hb4 zenon_H32e zenon_H109 zenon_He7 zenon_Hff zenon_H2d8 zenon_H329 zenon_H2a5 zenon_H29 zenon_H129 zenon_H12b zenon_Hc8 zenon_H2fc zenon_H1b1. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H118. zenon_intro zenon_H18a. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.76 apply (zenon_L193_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.76 apply (zenon_L194_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.76 apply (zenon_L195_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.76 apply (zenon_L117_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.76 apply (zenon_L155_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.76 apply (zenon_L156_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.76 apply (zenon_L460_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.76 apply (zenon_L159_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.76 apply (zenon_L129_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.76 apply (zenon_L162_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.76 apply (zenon_L131_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.76 apply (zenon_L132_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.76 apply (zenon_L202_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_H30. zenon_intro zenon_H1af. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_H14e. zenon_intro zenon_H1b0. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb3. zenon_intro zenon_H1b1. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H32e); [ zenon_intro zenon_H26f | zenon_intro zenon_H32f ]. % 8.54/8.76 apply (zenon_L461_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H32f); [ zenon_intro zenon_H87 | zenon_intro zenon_H330 ]. % 8.54/8.76 apply (zenon_L35_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H330); [ zenon_intro zenon_H27e | zenon_intro zenon_H1a9 ]. % 8.54/8.76 apply (zenon_L462_); trivial. % 8.54/8.76 apply (zenon_L133_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.76 apply (zenon_L443_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.76 apply (zenon_L444_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.76 apply (zenon_L171_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.76 apply (zenon_L172_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.76 apply (zenon_L173_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.76 apply (zenon_L463_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.76 apply (zenon_L175_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.76 apply (zenon_L176_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.76 apply (zenon_L146_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.76 apply (zenon_L177_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.76 apply (zenon_L148_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.76 apply (zenon_L151_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.76 apply (zenon_L152_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.76 apply (zenon_L153_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.76 apply (zenon_L182_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.76 apply (zenon_L356_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.76 apply (zenon_L446_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.76 apply (zenon_L447_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.76 apply (zenon_L464_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.76 apply (zenon_L465_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.76 apply (zenon_L188_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.76 apply (zenon_L468_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.76 apply (zenon_L190_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.76 apply (zenon_L212_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.76 apply (zenon_L363_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.76 apply (zenon_L214_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.76 apply (zenon_L241_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.76 apply (zenon_L242_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.76 apply (zenon_L366_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.76 apply (zenon_L272_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.76 apply (zenon_L273_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.76 apply (zenon_L367_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.76 apply (zenon_L451_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.76 apply (zenon_L452_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.76 apply (zenon_L223_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.76 apply (zenon_L275_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.76 apply (zenon_L225_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.76 apply (zenon_L372_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.76 apply (zenon_L469_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.76 apply (zenon_L470_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.76 apply (zenon_L475_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.76 apply (zenon_L378_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.76 apply (zenon_L453_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.76 apply (zenon_L380_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.76 apply (zenon_L381_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.76 apply (zenon_L382_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.76 apply (zenon_L383_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.76 apply (zenon_L385_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.76 apply (zenon_L454_); trivial. % 8.54/8.76 apply (zenon_L455_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H41. zenon_intro zenon_H4a. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H4a). zenon_intro zenon_H154. zenon_intro zenon_H2c3. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.76 apply (zenon_L193_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.76 apply (zenon_L194_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.76 apply (zenon_L116_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.76 apply (zenon_L117_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.76 apply (zenon_L155_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.76 apply (zenon_L156_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.76 apply (zenon_L277_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.76 apply (zenon_L159_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.76 apply (zenon_L129_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.76 apply (zenon_L278_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.76 apply (zenon_L131_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.76 apply (zenon_L132_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.76 apply (zenon_L202_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_H30. zenon_intro zenon_H1af. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_H14e. zenon_intro zenon_H1b0. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb3. zenon_intro zenon_H1b1. % 8.54/8.76 apply (zenon_L476_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.76 apply (zenon_L443_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.76 apply (zenon_L444_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.76 apply (zenon_L171_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.76 apply (zenon_L172_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.76 apply (zenon_L173_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.76 apply (zenon_L463_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.76 apply (zenon_L175_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.76 apply (zenon_L176_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.76 apply (zenon_L146_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.76 apply (zenon_L177_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_H29. zenon_intro zenon_H1c9. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1c9). zenon_intro zenon_H15a. zenon_intro zenon_H19f. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H19f). zenon_intro zenon_H7e. zenon_intro zenon_Hc8. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.54/8.76 apply (zenon_L4_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.54/8.76 apply (zenon_L82_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.54/8.76 apply (zenon_L83_); trivial. % 8.54/8.76 apply (zenon_L467_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.76 apply (zenon_L205_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.76 apply (zenon_L152_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.76 apply (zenon_L153_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.76 apply (zenon_L208_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.76 apply (zenon_L356_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.76 apply (zenon_L446_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.76 apply (zenon_L447_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.76 apply (zenon_L464_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.76 apply (zenon_L465_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.76 apply (zenon_L188_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.76 apply (zenon_L468_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.76 apply (zenon_L190_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.76 apply (zenon_L212_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.76 apply (zenon_L363_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.76 apply (zenon_L279_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.76 apply (zenon_L241_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.76 apply (zenon_L242_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.76 apply (zenon_L366_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.76 apply (zenon_L272_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.76 apply (zenon_L219_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.76 apply (zenon_L367_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.76 apply (zenon_L451_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.76 apply (zenon_L452_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.76 apply (zenon_L223_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.76 apply (zenon_L281_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.76 apply (zenon_L225_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.76 apply (zenon_L372_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.76 apply (zenon_L469_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.76 apply (zenon_L470_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H219). zenon_intro zenon_H1b1. zenon_intro zenon_H21a. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H21a). zenon_intro zenon_Hb3. zenon_intro zenon_H189. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H15a. zenon_intro zenon_H29. % 8.54/8.76 apply (zenon_L476_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.76 apply (zenon_L378_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.76 apply (zenon_L453_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.76 apply (zenon_L380_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.76 apply (zenon_L381_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.76 apply (zenon_L382_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.76 apply (zenon_L383_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.76 apply (zenon_L385_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.76 apply (zenon_L454_); trivial. % 8.54/8.76 apply (zenon_L455_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H4c. zenon_intro zenon_H57. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.76 apply (zenon_L193_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.76 apply (zenon_L194_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.76 apply (zenon_L282_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H17e). zenon_intro zenon_H1e. zenon_intro zenon_H17f. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H17f). zenon_intro zenon_H1e. zenon_intro zenon_H180. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H14e. zenon_intro zenon_H30. % 8.54/8.76 apply (zenon_L477_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.76 apply (zenon_L155_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.76 apply (zenon_L156_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.76 apply (zenon_L283_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.76 apply (zenon_L159_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.76 apply (zenon_L129_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.76 apply (zenon_L284_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.76 apply (zenon_L131_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.76 apply (zenon_L285_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.76 apply (zenon_L202_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_H30. zenon_intro zenon_H1af. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_H14e. zenon_intro zenon_H1b0. % 8.54/8.76 apply (zenon_L477_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.76 apply (zenon_L443_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.76 apply (zenon_L444_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.76 apply (zenon_L171_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.76 apply (zenon_L172_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.76 apply (zenon_L286_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.76 apply (zenon_L463_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.76 apply (zenon_L175_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.76 apply (zenon_L176_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.76 apply (zenon_L146_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.76 apply (zenon_L177_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.76 apply (zenon_L411_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.76 apply (zenon_L151_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.76 apply (zenon_L152_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.76 apply (zenon_L287_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.76 apply (zenon_L182_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.76 apply (zenon_L356_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.76 apply (zenon_L446_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.76 apply (zenon_L447_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.76 apply (zenon_L464_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.76 apply (zenon_L465_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.76 apply (zenon_L188_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_Hc8. zenon_intro zenon_H1f1. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1f1). zenon_intro zenon_H7e. zenon_intro zenon_H180. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H14e. zenon_intro zenon_H30. % 8.54/8.76 apply (zenon_L478_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.76 apply (zenon_L190_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.76 apply (zenon_L212_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.76 apply (zenon_L363_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.76 apply (zenon_L214_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.76 apply (zenon_L241_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.76 apply (zenon_L242_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.76 apply (zenon_L366_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.76 apply (zenon_L272_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.76 apply (zenon_L219_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.76 apply (zenon_L367_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.76 apply (zenon_L451_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.76 apply (zenon_L452_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.76 apply (zenon_L223_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.76 apply (zenon_L224_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.76 apply (zenon_L293_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.76 apply (zenon_L372_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.76 apply (zenon_L469_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.76 apply (zenon_L470_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.76 apply (zenon_L414_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.76 apply (zenon_L378_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.76 apply (zenon_L453_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.76 apply (zenon_L380_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.76 apply (zenon_L381_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.76 apply (zenon_L382_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.76 apply (zenon_L383_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.76 apply (zenon_L385_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.76 apply (zenon_L454_); trivial. % 8.54/8.76 apply (zenon_L455_); trivial. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H59. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.76 apply (zenon_L193_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.76 apply (zenon_L194_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.76 apply (zenon_L116_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.76 apply (zenon_L417_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.76 apply (zenon_L155_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.76 apply (zenon_L156_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H187). zenon_intro zenon_H1d. zenon_intro zenon_H188. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H188). zenon_intro zenon_Hac. zenon_intro zenon_H189. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H15a. zenon_intro zenon_H29. % 8.54/8.76 apply (zenon_L480_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.76 apply (zenon_L333_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.76 apply (zenon_L129_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.76 apply (zenon_L162_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.76 apply (zenon_L131_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.76 apply (zenon_L296_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.76 apply (zenon_L202_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.76 apply (zenon_L459_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.76 apply (zenon_L443_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.76 apply (zenon_L444_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.76 apply (zenon_L171_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.76 apply (zenon_L172_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.76 apply (zenon_L173_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.76 apply (zenon_L419_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.76 apply (zenon_L175_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.76 apply (zenon_L176_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.76 apply (zenon_L146_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.76 apply (zenon_L334_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_H29. zenon_intro zenon_H1c9. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H1c9). zenon_intro zenon_H15a. zenon_intro zenon_H19f. % 8.54/8.76 apply (zenon_L480_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.76 apply (zenon_L205_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.76 apply (zenon_L152_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.76 apply (zenon_L297_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.76 apply (zenon_L298_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.76 apply (zenon_L356_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.76 apply (zenon_L446_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.76 apply (zenon_L447_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.76 apply (zenon_L464_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.76 apply (zenon_L465_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.76 apply (zenon_L188_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.76 apply (zenon_L422_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.76 apply (zenon_L190_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.76 apply (zenon_L212_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.76 apply (zenon_L363_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.76 apply (zenon_L335_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.76 apply (zenon_L241_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.76 apply (zenon_L242_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.76 apply (zenon_L366_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.76 apply (zenon_L299_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.76 apply (zenon_L300_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.76 apply (zenon_L423_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.76 apply (zenon_L451_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.76 apply (zenon_L452_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.76 apply (zenon_L223_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.76 apply (zenon_L224_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.76 apply (zenon_L225_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.76 apply (zenon_L372_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.76 apply (zenon_L469_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.76 apply (zenon_L470_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.76 apply (zenon_L482_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.76 apply (zenon_L378_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.76 apply (zenon_L453_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.76 apply (zenon_L380_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.76 apply (zenon_L381_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.76 apply (zenon_L382_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.76 apply (zenon_L383_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.76 apply (zenon_L385_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.76 apply (zenon_L454_); trivial. % 8.54/8.76 apply (zenon_L455_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.54/8.76 apply (zenon_L74_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.54/8.76 apply (zenon_L75_); trivial. % 8.54/8.76 apply (zenon_L384_); trivial. % 8.54/8.76 (* end of lemma zenon_L483_ *) % 8.54/8.76 assert (zenon_L484_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((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) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.54/8.76 do 0 intro. intros zenon_H1d3 zenon_H2df zenon_H2f3 zenon_Hd0 zenon_H16d zenon_H1f zenon_H270 zenon_H2a4 zenon_H2b5 zenon_H2c0 zenon_H169 zenon_H1dc zenon_H2a1 zenon_H295 zenon_H19a zenon_H2c9 zenon_Hb7 zenon_H6c zenon_H74 zenon_H150 zenon_H282 zenon_H137 zenon_H27f zenon_H2e8 zenon_H285 zenon_Hf3 zenon_Hf9 zenon_H2a3 zenon_Hf8 zenon_H164 zenon_H1dd zenon_H2e2 zenon_H2bf zenon_H124 zenon_H11f zenon_H36 zenon_H2fc zenon_H12b zenon_H129 zenon_H2a5 zenon_H329 zenon_H2d8 zenon_Hff zenon_He7 zenon_H109 zenon_H32e zenon_Hb4 zenon_H10c zenon_H145 zenon_H2d4 zenon_H2d2 zenon_H29f zenon_H2a2 zenon_H3a zenon_Hc5 zenon_H170 zenon_H153 zenon_H22e zenon_H25 zenon_H31 zenon_H127 zenon_H78 zenon_H7d zenon_H1f6 zenon_Hc2 zenon_Hab zenon_H2b zenon_H197 zenon_H67 zenon_H2b8 zenon_Ha3 zenon_H192 zenon_Ha8 zenon_H1d7 zenon_H22d zenon_H173 zenon_Hc8 zenon_H1d9 zenon_H1b1. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c1 ]. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.54/8.76 apply (zenon_L303_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H118. zenon_intro zenon_H18a. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.76 apply (zenon_L308_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.76 apply (zenon_L309_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.76 apply (zenon_L115_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.76 apply (zenon_L442_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.76 apply (zenon_L120_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.76 apply (zenon_L121_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.76 apply (zenon_L122_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.76 apply (zenon_L310_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.76 apply (zenon_L129_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.76 apply (zenon_L130_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.76 apply (zenon_L131_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.76 apply (zenon_L132_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.76 apply (zenon_L135_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.76 apply (zenon_L136_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.76 apply (zenon_L443_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.76 apply (zenon_L444_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.76 apply (zenon_L311_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.76 apply (zenon_L312_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.76 apply (zenon_L141_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.76 apply (zenon_L445_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.76 apply (zenon_L143_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.76 apply (zenon_L144_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.76 apply (zenon_L146_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.76 apply (zenon_L147_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.76 apply (zenon_L148_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.76 apply (zenon_L151_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.76 apply (zenon_L152_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.76 apply (zenon_L153_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.76 apply (zenon_L355_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.76 apply (zenon_L356_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.76 apply (zenon_L446_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.76 apply (zenon_L447_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.76 apply (zenon_L448_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.76 apply (zenon_L449_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.76 apply (zenon_L188_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.76 apply (zenon_L450_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.76 apply (zenon_L316_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.76 apply (zenon_L317_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.76 apply (zenon_L364_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.76 apply (zenon_L365_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.76 apply (zenon_L241_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.76 apply (zenon_L242_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.76 apply (zenon_L366_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.76 apply (zenon_L272_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.76 apply (zenon_L273_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.76 apply (zenon_L367_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.76 apply (zenon_L451_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.76 apply (zenon_L452_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.76 apply (zenon_L322_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.76 apply (zenon_L275_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.76 apply (zenon_L371_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.76 apply (zenon_L373_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.76 apply (zenon_L374_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.76 apply (zenon_L408_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.76 apply (zenon_L377_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.76 apply (zenon_L378_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.76 apply (zenon_L453_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.76 apply (zenon_L380_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.76 apply (zenon_L381_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.76 apply (zenon_L382_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.76 apply (zenon_L383_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.76 apply (zenon_L385_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.76 apply (zenon_L454_); trivial. % 8.54/8.76 apply (zenon_L455_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H41. zenon_intro zenon_H4a. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H4a). zenon_intro zenon_H154. zenon_intro zenon_H2c3. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.76 apply (zenon_L308_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.76 apply (zenon_L309_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.76 apply (zenon_L116_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.76 apply (zenon_L442_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.76 apply (zenon_L120_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.76 apply (zenon_L121_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.76 apply (zenon_L277_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.76 apply (zenon_L310_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.76 apply (zenon_L129_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.76 apply (zenon_L278_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.76 apply (zenon_L131_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.76 apply (zenon_L132_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.76 apply (zenon_L135_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.76 apply (zenon_L136_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.76 apply (zenon_L443_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.76 apply (zenon_L444_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.76 apply (zenon_L311_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.76 apply (zenon_L312_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.76 apply (zenon_L141_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.76 apply (zenon_L445_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.76 apply (zenon_L143_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.76 apply (zenon_L144_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.76 apply (zenon_L146_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.76 apply (zenon_L147_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.76 apply (zenon_L456_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.76 apply (zenon_L151_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.76 apply (zenon_L152_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.76 apply (zenon_L153_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.76 apply (zenon_L355_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.76 apply (zenon_L356_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.76 apply (zenon_L446_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.76 apply (zenon_L447_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.76 apply (zenon_L448_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.76 apply (zenon_L449_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.76 apply (zenon_L188_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.76 apply (zenon_L450_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.76 apply (zenon_L316_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.76 apply (zenon_L317_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.76 apply (zenon_L364_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.76 apply (zenon_L279_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.76 apply (zenon_L241_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.76 apply (zenon_L242_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.76 apply (zenon_L366_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.76 apply (zenon_L272_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.76 apply (zenon_L457_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.76 apply (zenon_L367_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.76 apply (zenon_L451_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.76 apply (zenon_L452_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.76 apply (zenon_L322_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.76 apply (zenon_L281_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.76 apply (zenon_L371_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.76 apply (zenon_L373_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.76 apply (zenon_L374_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.76 apply (zenon_L408_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.76 apply (zenon_L377_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.76 apply (zenon_L378_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.76 apply (zenon_L453_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.76 apply (zenon_L380_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.76 apply (zenon_L381_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.76 apply (zenon_L382_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.76 apply (zenon_L383_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.76 apply (zenon_L385_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.76 apply (zenon_L454_); trivial. % 8.54/8.76 apply (zenon_L455_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H4c. zenon_intro zenon_H57. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.76 apply (zenon_L308_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.76 apply (zenon_L309_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.76 apply (zenon_L282_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.76 apply (zenon_L442_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.76 apply (zenon_L120_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.76 apply (zenon_L121_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.76 apply (zenon_L283_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.76 apply (zenon_L310_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.76 apply (zenon_L129_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.76 apply (zenon_L284_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.76 apply (zenon_L131_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.76 apply (zenon_L285_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.76 apply (zenon_L135_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.76 apply (zenon_L136_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.76 apply (zenon_L443_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.76 apply (zenon_L444_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.76 apply (zenon_L311_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.76 apply (zenon_L312_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.76 apply (zenon_L286_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.76 apply (zenon_L445_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.76 apply (zenon_L143_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.76 apply (zenon_L144_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.76 apply (zenon_L146_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.76 apply (zenon_L147_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.76 apply (zenon_L411_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.76 apply (zenon_L151_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.76 apply (zenon_L152_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.76 apply (zenon_L287_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.76 apply (zenon_L355_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.76 apply (zenon_L356_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.76 apply (zenon_L446_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.76 apply (zenon_L447_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.76 apply (zenon_L448_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.76 apply (zenon_L449_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.76 apply (zenon_L188_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.76 apply (zenon_L450_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.76 apply (zenon_L316_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.76 apply (zenon_L317_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.76 apply (zenon_L364_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.76 apply (zenon_L458_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.76 apply (zenon_L241_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.76 apply (zenon_L242_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.76 apply (zenon_L366_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.76 apply (zenon_L272_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.76 apply (zenon_L457_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.76 apply (zenon_L367_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.76 apply (zenon_L451_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.76 apply (zenon_L452_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.76 apply (zenon_L322_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.76 apply (zenon_L323_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.76 apply (zenon_L293_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.76 apply (zenon_L373_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.76 apply (zenon_L374_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.76 apply (zenon_L408_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.76 apply (zenon_L414_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.76 apply (zenon_L378_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.76 apply (zenon_L453_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.76 apply (zenon_L380_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.76 apply (zenon_L381_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.76 apply (zenon_L382_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.76 apply (zenon_L383_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.76 apply (zenon_L385_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.76 apply (zenon_L454_); trivial. % 8.54/8.76 apply (zenon_L455_); trivial. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 8.54/8.76 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H59. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.76 apply (zenon_L308_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.76 apply (zenon_L309_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.76 apply (zenon_L116_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.76 apply (zenon_L417_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.76 apply (zenon_L120_); trivial. % 8.54/8.76 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.77 apply (zenon_L121_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.77 apply (zenon_L122_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.77 apply (zenon_L333_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.77 apply (zenon_L129_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.77 apply (zenon_L130_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.77 apply (zenon_L131_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.77 apply (zenon_L296_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.77 apply (zenon_L135_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.77 apply (zenon_L459_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.77 apply (zenon_L443_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.77 apply (zenon_L444_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.77 apply (zenon_L311_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.77 apply (zenon_L312_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.77 apply (zenon_L141_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.77 apply (zenon_L419_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.77 apply (zenon_L143_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.77 apply (zenon_L144_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.77 apply (zenon_L146_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.77 apply (zenon_L334_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.77 apply (zenon_L456_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.77 apply (zenon_L151_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.77 apply (zenon_L152_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.77 apply (zenon_L297_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.77 apply (zenon_L298_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.77 apply (zenon_L356_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.77 apply (zenon_L446_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.77 apply (zenon_L447_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.77 apply (zenon_L448_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.77 apply (zenon_L449_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.77 apply (zenon_L188_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.77 apply (zenon_L422_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.77 apply (zenon_L316_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.77 apply (zenon_L317_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.77 apply (zenon_L364_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.77 apply (zenon_L335_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.77 apply (zenon_L241_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.77 apply (zenon_L242_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.77 apply (zenon_L366_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.77 apply (zenon_L299_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.77 apply (zenon_L300_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.77 apply (zenon_L423_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.77 apply (zenon_L451_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.77 apply (zenon_L452_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.77 apply (zenon_L322_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.77 apply (zenon_L323_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.77 apply (zenon_L425_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.77 apply (zenon_L373_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.77 apply (zenon_L374_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.77 apply (zenon_L408_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.77 apply (zenon_L377_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.77 apply (zenon_L378_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.77 apply (zenon_L453_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.77 apply (zenon_L380_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.77 apply (zenon_L381_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.77 apply (zenon_L382_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.77 apply (zenon_L383_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.77 apply (zenon_L385_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.77 apply (zenon_L454_); trivial. % 8.54/8.77 apply (zenon_L455_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.54/8.77 apply (zenon_L75_); trivial. % 8.54/8.77 apply (zenon_L384_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H29 | zenon_intro zenon_H2c2 ]. % 8.54/8.77 apply (zenon_L483_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2c2); [ zenon_intro zenon_H3b | zenon_intro zenon_H98 ]. % 8.54/8.77 apply (zenon_L112_); trivial. % 8.54/8.77 apply (zenon_L375_); trivial. % 8.54/8.77 (* end of lemma zenon_L484_ *) % 8.54/8.77 assert (zenon_L485_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((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) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e2))) -> False). % 8.54/8.77 do 0 intro. intros zenon_H322 zenon_H105 zenon_He4 zenon_H11e zenon_H16d zenon_H5a zenon_Hbf zenon_H2a zenon_H303 zenon_H1d3 zenon_H2df zenon_H2f3 zenon_Hd0 zenon_H1f zenon_H270 zenon_H2a4 zenon_H2b5 zenon_H2c0 zenon_H169 zenon_H1dc zenon_H2a1 zenon_H295 zenon_H19a zenon_H2c9 zenon_Hb7 zenon_H6c zenon_H74 zenon_H150 zenon_H282 zenon_H137 zenon_H27f zenon_H2e8 zenon_H285 zenon_Hf3 zenon_Hf9 zenon_H2a3 zenon_Hf8 zenon_H164 zenon_H1dd zenon_H2e2 zenon_H2bf zenon_H124 zenon_H11f zenon_H36 zenon_H2fc zenon_H12b zenon_H129 zenon_H2a5 zenon_H329 zenon_H2d8 zenon_Hff zenon_He7 zenon_H109 zenon_H32e zenon_Hb4 zenon_H10c zenon_H145 zenon_H2d4 zenon_H2d2 zenon_H29f zenon_H2a2 zenon_H3a zenon_Hc5 zenon_H170 zenon_H153 zenon_H22e zenon_H25 zenon_H31 zenon_H127 zenon_H1f6 zenon_Hc2 zenon_Hab zenon_H2b zenon_H197 zenon_H67 zenon_H2b8 zenon_Ha3 zenon_H192 zenon_Ha8 zenon_H1d7 zenon_H22d zenon_H173 zenon_Hc8 zenon_H1d9 zenon_Hac zenon_Hba zenon_H78 zenon_H24 zenon_H7d. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.54/8.77 apply (zenon_L79_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.54/8.77 apply (zenon_L84_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.54/8.77 apply (zenon_L46_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.54/8.77 apply (zenon_L427_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.54/8.77 apply (zenon_L426_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.54/8.77 apply (zenon_L31_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a3); [ zenon_intro zenon_H274 | zenon_intro zenon_H2b2 ]. % 8.54/8.77 apply (zenon_L428_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H2b3 ]. % 8.54/8.77 apply (zenon_L31_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H196 | zenon_intro zenon_H1b1 ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.54/8.77 apply (zenon_L250_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.54/8.77 apply (zenon_L307_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.54/8.77 apply (zenon_L433_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.54/8.77 apply (zenon_L303_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.54/8.77 apply (zenon_L434_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.54/8.77 apply (zenon_L108_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H30 | zenon_intro zenon_H106 ]. % 8.54/8.77 apply (zenon_L66_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H107 ]. % 8.54/8.77 apply (zenon_L107_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfe | zenon_intro zenon_H103 ]. % 8.54/8.77 apply (zenon_L441_); trivial. % 8.54/8.77 apply (zenon_L89_); trivial. % 8.54/8.77 apply (zenon_L484_); trivial. % 8.54/8.77 apply (zenon_L471_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.54/8.77 apply (zenon_L128_); trivial. % 8.54/8.77 apply (zenon_L441_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.54/8.77 apply (zenon_L18_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.54/8.77 apply (zenon_L22_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.54/8.77 apply (zenon_L79_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.54/8.77 apply (zenon_L426_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.54/8.77 apply (zenon_L31_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a3); [ zenon_intro zenon_H274 | zenon_intro zenon_H2b2 ]. % 8.54/8.77 apply (zenon_L428_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H2b3 ]. % 8.54/8.77 apply (zenon_L31_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H196 | zenon_intro zenon_H1b1 ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.54/8.77 apply (zenon_L44_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.54/8.77 apply (zenon_L395_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.54/8.77 apply (zenon_L433_); trivial. % 8.54/8.77 apply (zenon_L107_); trivial. % 8.54/8.77 apply (zenon_L484_); trivial. % 8.54/8.77 apply (zenon_L109_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.54/8.77 apply (zenon_L128_); trivial. % 8.54/8.77 apply (zenon_L81_); trivial. % 8.54/8.77 (* end of lemma zenon_L485_ *) % 8.54/8.77 assert (zenon_L486_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 8.54/8.77 do 0 intro. intros zenon_H150 zenon_H31 zenon_Hd6 zenon_H74 zenon_H2a zenon_Hc8 zenon_H7d zenon_H14e zenon_H67. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.54/8.77 apply (zenon_L87_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.54/8.77 apply (zenon_L20_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.54/8.77 apply (zenon_L44_); trivial. % 8.54/8.77 apply (zenon_L94_); trivial. % 8.54/8.77 (* end of lemma zenon_L486_ *) % 8.54/8.77 assert (zenon_L487_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 8.54/8.77 do 0 intro. intros zenon_H2a1 zenon_He4 zenon_H5a zenon_H10c zenon_H145 zenon_Ha8 zenon_H2d2 zenon_Hba zenon_Ha3 zenon_H16d zenon_H27f zenon_H322 zenon_Hd0 zenon_H153 zenon_H105 zenon_H6c zenon_H24 zenon_H150 zenon_H31 zenon_H74 zenon_H2a zenon_Hc8 zenon_H7d zenon_H14e zenon_H67. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H30 | zenon_intro zenon_H106 ]. % 8.54/8.77 apply (zenon_L303_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H107 ]. % 8.54/8.77 apply (zenon_L486_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfe | zenon_intro zenon_H103 ]. % 8.54/8.77 apply (zenon_L441_); trivial. % 8.54/8.77 apply (zenon_L89_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.54/8.77 apply (zenon_L18_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.54/8.77 apply (zenon_L22_); trivial. % 8.54/8.77 apply (zenon_L486_); trivial. % 8.54/8.77 (* end of lemma zenon_L487_ *) % 8.54/8.77 assert (zenon_L488_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (op (e0) (e0))) = (e0))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 8.54/8.77 do 0 intro. intros zenon_H2a4 zenon_H12e zenon_Ha8 zenon_Hcb zenon_H29f zenon_H98 zenon_H30 zenon_Hc2. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a4); [ zenon_intro zenon_H26f | zenon_intro zenon_H2ad ]. % 8.54/8.77 apply (zenon_L461_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H274 | zenon_intro zenon_H2ae ]. % 8.54/8.77 apply (zenon_L428_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H276 | zenon_intro zenon_H103 ]. % 8.54/8.77 apply (zenon_L399_); trivial. % 8.54/8.77 apply (zenon_L201_); trivial. % 8.54/8.77 (* end of lemma zenon_L488_ *) % 8.54/8.77 assert (zenon_L489_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.54/8.77 do 0 intro. intros zenon_H331 zenon_Hc2 zenon_H30 zenon_Hb4 zenon_H87 zenon_H57 zenon_Heb zenon_H98. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H331); [ zenon_intro zenon_H103 | zenon_intro zenon_H332 ]. % 8.54/8.77 apply (zenon_L201_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H332); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H333 ]. % 8.54/8.77 apply (zenon_L35_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H333); [ zenon_intro zenon_H195 | zenon_intro zenon_H5a ]. % 8.54/8.77 apply (zenon_L409_); trivial. % 8.54/8.77 apply (zenon_L53_); trivial. % 8.54/8.77 (* end of lemma zenon_L489_ *) % 8.54/8.77 assert (zenon_L490_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 8.54/8.77 do 0 intro. intros zenon_Hba zenon_Heb zenon_H57 zenon_Hb4 zenon_H30 zenon_Hc2 zenon_H331 zenon_Ha3 zenon_H2a zenon_H2d2 zenon_H98 zenon_H108 zenon_Ha8. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.54/8.77 apply (zenon_L489_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.54/8.77 apply (zenon_L31_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.54/8.77 apply (zenon_L358_); trivial. % 8.54/8.77 apply (zenon_L471_); trivial. % 8.54/8.77 (* end of lemma zenon_L490_ *) % 8.54/8.77 assert (zenon_L491_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 8.54/8.77 do 0 intro. intros zenon_Hba zenon_Hc2 zenon_Hac zenon_Ha3 zenon_H2a zenon_H2d2 zenon_H98 zenon_H108 zenon_Ha8. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.54/8.77 apply (zenon_L426_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.54/8.77 apply (zenon_L31_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.54/8.77 apply (zenon_L358_); trivial. % 8.54/8.77 apply (zenon_L471_); trivial. % 8.54/8.77 (* end of lemma zenon_L491_ *) % 8.54/8.77 assert (zenon_L492_ : (~((op (e3) (op (e3) (e3))) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> False). % 8.54/8.77 do 0 intro. intros zenon_H59 zenon_H98 zenon_He8. % 8.54/8.77 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (op (e3) (e3))) = (e3))). % 8.54/8.77 intro zenon_D_pnotp. % 8.54/8.77 apply zenon_H59. % 8.54/8.77 rewrite <- zenon_D_pnotp. % 8.54/8.77 exact zenon_H98. % 8.54/8.77 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.77 cut (((op (e3) (e2)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H334]. % 8.54/8.77 congruence. % 8.54/8.77 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 8.54/8.77 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((op (e3) (e2)) = (op (e3) (op (e3) (e3))))). % 8.54/8.77 intro zenon_D_pnotp. % 8.54/8.77 apply zenon_H334. % 8.54/8.77 rewrite <- zenon_D_pnotp. % 8.54/8.77 exact zenon_H5c. % 8.54/8.77 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 8.54/8.77 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H335]. % 8.54/8.77 congruence. % 8.54/8.77 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H321]. % 8.54/8.77 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.77 congruence. % 8.54/8.77 apply zenon_H58. apply refl_equal. % 8.54/8.77 exact (zenon_H321 zenon_He8). % 8.54/8.77 apply zenon_H5d. apply refl_equal. % 8.54/8.77 apply zenon_H5d. apply refl_equal. % 8.54/8.77 apply zenon_H58. apply refl_equal. % 8.54/8.77 (* end of lemma zenon_L492_ *) % 8.54/8.77 assert (zenon_L493_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((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 (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.54/8.77 do 0 intro. intros zenon_H22d zenon_H78 zenon_H329 zenon_Ha8 zenon_H2d2 zenon_Ha3 zenon_Hc2 zenon_Hba zenon_H31 zenon_H2a2 zenon_H10c zenon_H145 zenon_H7d zenon_H170 zenon_Hb7 zenon_H74 zenon_Hab zenon_H153 zenon_Hc5 zenon_Hb4 zenon_H331 zenon_H11e zenon_H137 zenon_H29f zenon_H2a4 zenon_H2a5 zenon_H36 zenon_H2a zenon_H12b zenon_Hc8 zenon_Heb zenon_H98. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H118. zenon_intro zenon_H18a. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.54/8.77 apply (zenon_L79_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.54/8.77 apply (zenon_L488_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.54/8.77 apply (zenon_L70_); trivial. % 8.54/8.77 apply (zenon_L394_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.54/8.77 apply (zenon_L10_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H4c. zenon_intro zenon_H57. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.54/8.77 apply (zenon_L4_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.54/8.77 apply (zenon_L305_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.54/8.77 apply (zenon_L46_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.54/8.77 apply (zenon_L426_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.54/8.77 apply (zenon_L31_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.54/8.77 apply (zenon_L32_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_H24 | zenon_intro zenon_Hc6 ]. % 8.54/8.77 apply (zenon_L303_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Had | zenon_intro zenon_Hc7 ]. % 8.54/8.77 apply (zenon_L36_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H80 | zenon_intro zenon_Hc3 ]. % 8.54/8.77 apply (zenon_L102_); trivial. % 8.54/8.77 apply (zenon_L42_); trivial. % 8.54/8.77 apply (zenon_L490_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.54/8.77 apply (zenon_L100_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.54/8.77 apply (zenon_L84_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.54/8.77 apply (zenon_L46_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.54/8.77 apply (zenon_L489_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.54/8.77 apply (zenon_L31_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.54/8.77 apply (zenon_L32_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_H24 | zenon_intro zenon_Hc6 ]. % 8.54/8.77 apply (zenon_L303_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Had | zenon_intro zenon_Hc7 ]. % 8.54/8.77 apply (zenon_L36_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H80 | zenon_intro zenon_Hc3 ]. % 8.54/8.77 apply (zenon_L102_); trivial. % 8.54/8.77 apply (zenon_L111_); trivial. % 8.54/8.77 apply (zenon_L490_); trivial. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H59. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.54/8.77 apply (zenon_L4_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hfe | zenon_intro zenon_H32a ]. % 8.54/8.77 apply (zenon_L394_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H108 | zenon_intro zenon_H32b ]. % 8.54/8.77 apply (zenon_L491_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H3c | zenon_intro zenon_He8 ]. % 8.54/8.77 apply (zenon_L75_); trivial. % 8.54/8.77 apply (zenon_L492_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.54/8.77 apply (zenon_L83_); trivial. % 8.54/8.77 apply (zenon_L416_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.54/8.77 apply (zenon_L5_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.54/8.77 apply (zenon_L75_); trivial. % 8.54/8.77 apply (zenon_L53_); trivial. % 8.54/8.77 (* end of lemma zenon_L493_ *) % 8.54/8.77 assert (zenon_L494_ : (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((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)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (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) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((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 (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 8.54/8.77 do 0 intro. intros zenon_H67 zenon_H150 zenon_H6c zenon_H105 zenon_Hd0 zenon_H322 zenon_H27f zenon_H16d zenon_He4 zenon_H2a1 zenon_Hbf zenon_H303 zenon_H1d3 zenon_H2df zenon_H2f3 zenon_H1f zenon_H270 zenon_H2b5 zenon_H2c0 zenon_H169 zenon_H1dc zenon_H295 zenon_H19a zenon_H2c9 zenon_H282 zenon_H2e8 zenon_H285 zenon_Hf3 zenon_Hf9 zenon_H2a3 zenon_Hf8 zenon_H164 zenon_H1dd zenon_H2e2 zenon_H2bf zenon_H124 zenon_H11f zenon_H2fc zenon_H129 zenon_H2d8 zenon_Hff zenon_He7 zenon_H109 zenon_H32e zenon_H2d4 zenon_H3a zenon_H22e zenon_H25 zenon_H127 zenon_H1f6 zenon_H197 zenon_H2b8 zenon_H192 zenon_H1d7 zenon_H1d9 zenon_H2b zenon_H173 zenon_H22d zenon_H78 zenon_H329 zenon_Ha8 zenon_H2d2 zenon_Ha3 zenon_Hc2 zenon_Hba zenon_H31 zenon_H2a2 zenon_H10c zenon_H145 zenon_H7d zenon_H170 zenon_Hb7 zenon_H74 zenon_Hab zenon_H153 zenon_Hc5 zenon_Hb4 zenon_H331 zenon_H11e zenon_H137 zenon_H29f zenon_H2a4 zenon_H2a5 zenon_H36 zenon_H2a zenon_H12b zenon_Hc8 zenon_Heb. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c1 ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.54/8.77 apply (zenon_L303_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.54/8.77 apply (zenon_L5_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.54/8.77 apply (zenon_L75_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.54/8.77 apply (zenon_L2_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.54/8.77 apply (zenon_L485_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.54/8.77 apply (zenon_L83_); trivial. % 8.54/8.77 apply (zenon_L487_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H29 | zenon_intro zenon_H2c2 ]. % 8.54/8.77 apply (zenon_L3_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2c2); [ zenon_intro zenon_H3b | zenon_intro zenon_H98 ]. % 8.54/8.77 apply (zenon_L112_); trivial. % 8.54/8.77 apply (zenon_L493_); trivial. % 8.54/8.77 (* end of lemma zenon_L494_ *) % 8.54/8.77 assert (zenon_L495_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((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) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.54/8.77 do 0 intro. intros zenon_H90 zenon_H300 zenon_H2f8 zenon_H134 zenon_H336 zenon_H94 zenon_Heb zenon_H11e zenon_H331 zenon_Hba zenon_H303 zenon_Hbf zenon_He4 zenon_H322 zenon_H105 zenon_H1d3 zenon_H2df zenon_H2f3 zenon_Hd0 zenon_H16d zenon_H1f zenon_H270 zenon_H2a4 zenon_H2b5 zenon_H2c0 zenon_H169 zenon_H1dc zenon_H2a1 zenon_H295 zenon_H19a zenon_H2c9 zenon_Hb7 zenon_H6c zenon_H74 zenon_H150 zenon_H282 zenon_H137 zenon_H27f zenon_H2e8 zenon_H285 zenon_Hf3 zenon_Hf9 zenon_H2a3 zenon_Hf8 zenon_H164 zenon_H1dd zenon_H2e2 zenon_H2bf zenon_H124 zenon_H11f zenon_H36 zenon_H2fc zenon_H12b zenon_H129 zenon_H2a5 zenon_H329 zenon_H2d8 zenon_Hff zenon_He7 zenon_H109 zenon_H32e zenon_Hb4 zenon_H10c zenon_H145 zenon_H2d4 zenon_H2d2 zenon_H29f zenon_H2a2 zenon_H3a zenon_Hc5 zenon_H170 zenon_H153 zenon_H22e zenon_H25 zenon_H31 zenon_H127 zenon_H78 zenon_H7d zenon_H1f6 zenon_Hc2 zenon_Hab zenon_H2b zenon_H197 zenon_H67 zenon_H2b8 zenon_Ha3 zenon_H192 zenon_Ha8 zenon_H1d7 zenon_H22d zenon_H173 zenon_Hc8 zenon_H1d9. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H1d | zenon_intro zenon_H2f4 ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c1 ]. % 8.54/8.77 apply (zenon_L72_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H29 | zenon_intro zenon_H2c2 ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.54/8.77 apply (zenon_L73_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.54/8.77 apply (zenon_L74_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.54/8.77 apply (zenon_L75_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H118. zenon_intro zenon_H18a. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.54/8.77 apply (zenon_L76_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.54/8.77 apply (zenon_L77_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.54/8.77 apply (zenon_L78_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.54/8.77 apply (zenon_L79_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.54/8.77 apply (zenon_L80_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.54/8.77 apply (zenon_L70_); trivial. % 8.54/8.77 apply (zenon_L81_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H41. zenon_intro zenon_H4a. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H4a). zenon_intro zenon_H154. zenon_intro zenon_H2c3. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.54/8.77 apply (zenon_L1_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.54/8.77 apply (zenon_L82_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.54/8.77 apply (zenon_L83_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.54/8.77 apply (zenon_L79_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.54/8.77 apply (zenon_L80_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.54/8.77 apply (zenon_L84_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.54/8.77 apply (zenon_L85_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.54/8.77 apply (zenon_L86_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.54/8.77 apply (zenon_L73_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.54/8.77 apply (zenon_L90_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.54/8.77 apply (zenon_L92_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H30 | zenon_intro zenon_H106 ]. % 8.54/8.77 apply (zenon_L66_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H107 ]. % 8.54/8.77 apply (zenon_L95_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfe | zenon_intro zenon_H103 ]. % 8.54/8.77 apply (zenon_L96_); trivial. % 8.54/8.77 apply (zenon_L89_); trivial. % 8.54/8.77 apply (zenon_L98_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.54/8.77 apply (zenon_L77_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.54/8.77 apply (zenon_L78_); trivial. % 8.54/8.77 apply (zenon_L95_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H4c. zenon_intro zenon_H57. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.54/8.77 apply (zenon_L1_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.54/8.77 apply (zenon_L77_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.54/8.77 apply (zenon_L3_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.54/8.77 apply (zenon_L99_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H143 | zenon_intro zenon_H286 ]. % 8.54/8.77 apply (zenon_L100_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H165 | zenon_intro zenon_H287 ]. % 8.54/8.77 apply (zenon_L101_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H80 | zenon_intro zenon_H10f ]. % 8.54/8.77 apply (zenon_L102_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.54/8.77 apply (zenon_L44_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.54/8.77 apply (zenon_L103_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.54/8.77 apply (zenon_L104_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H2b6 ]. % 8.54/8.77 apply (zenon_L105_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H35 | zenon_intro zenon_H2b7 ]. % 8.54/8.77 apply (zenon_L106_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H108 | zenon_intro zenon_Hb3 ]. % 8.54/8.77 apply (zenon_L108_); trivial. % 8.54/8.77 apply (zenon_L109_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.54/8.77 apply (zenon_L100_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_H24 | zenon_intro zenon_Hc6 ]. % 8.54/8.77 apply (zenon_L72_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Had | zenon_intro zenon_Hc7 ]. % 8.54/8.77 apply (zenon_L110_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H80 | zenon_intro zenon_Hc3 ]. % 8.54/8.77 apply (zenon_L102_); trivial. % 8.54/8.77 apply (zenon_L111_); trivial. % 8.54/8.77 apply (zenon_L16_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2c2); [ zenon_intro zenon_H3b | zenon_intro zenon_H98 ]. % 8.54/8.77 apply (zenon_L112_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.54/8.77 apply (zenon_L73_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H118. zenon_intro zenon_H18a. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.77 apply (zenon_L113_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.77 apply (zenon_L114_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.77 apply (zenon_L116_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.77 apply (zenon_L118_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.77 apply (zenon_L120_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.77 apply (zenon_L121_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.77 apply (zenon_L122_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H1d1). zenon_intro zenon_H1d. zenon_intro zenon_H1d2. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H1d2). zenon_intro zenon_Hac. zenon_intro zenon_H1c7. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_Hf4. zenon_intro zenon_H35. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H331); [ zenon_intro zenon_H103 | zenon_intro zenon_H332 ]. % 8.54/8.77 apply (zenon_L123_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H332); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H333 ]. % 8.54/8.77 apply (zenon_L124_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H333); [ zenon_intro zenon_H195 | zenon_intro zenon_H5a ]. % 8.54/8.77 apply (zenon_L127_); trivial. % 8.54/8.77 apply (zenon_L53_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.77 apply (zenon_L129_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.77 apply (zenon_L130_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.77 apply (zenon_L131_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.77 apply (zenon_L132_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.77 apply (zenon_L135_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.77 apply (zenon_L136_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.77 apply (zenon_L137_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.77 apply (zenon_L138_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.77 apply (zenon_L139_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.77 apply (zenon_L140_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.77 apply (zenon_L141_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.77 apply (zenon_L142_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.77 apply (zenon_L143_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.77 apply (zenon_L144_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.77 apply (zenon_L146_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.77 apply (zenon_L147_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.77 apply (zenon_L148_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.77 apply (zenon_L151_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.77 apply (zenon_L152_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.77 apply (zenon_L153_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.77 apply (zenon_L355_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.77 apply (zenon_L356_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H35. zenon_intro zenon_H1e7. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_Hf4. zenon_intro zenon_H1d6. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H195. zenon_intro zenon_H98. % 8.54/8.77 apply (zenon_L127_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.77 apply (zenon_L357_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.77 apply (zenon_L186_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.77 apply (zenon_L360_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.77 apply (zenon_L188_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.77 apply (zenon_L361_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.77 apply (zenon_L316_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.77 apply (zenon_L362_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.77 apply (zenon_L364_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.77 apply (zenon_L365_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.77 apply (zenon_L241_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.77 apply (zenon_L242_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.77 apply (zenon_L366_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.77 apply (zenon_L272_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.77 apply (zenon_L273_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.77 apply (zenon_L367_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.77 apply (zenon_L369_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.77 apply (zenon_L370_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.77 apply (zenon_L274_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.77 apply (zenon_L275_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.77 apply (zenon_L371_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.77 apply (zenon_L373_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.77 apply (zenon_L374_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.77 apply (zenon_L376_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.77 apply (zenon_L377_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.77 apply (zenon_L378_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.77 apply (zenon_L379_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.77 apply (zenon_L380_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.77 apply (zenon_L381_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.77 apply (zenon_L382_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.77 apply (zenon_L383_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.77 apply (zenon_L386_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.77 apply (zenon_L387_); trivial. % 8.54/8.77 apply (zenon_L388_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H41. zenon_intro zenon_H4a. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H4a). zenon_intro zenon_H154. zenon_intro zenon_H2c3. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.77 apply (zenon_L113_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.77 apply (zenon_L114_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.77 apply (zenon_L116_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.77 apply (zenon_L118_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.77 apply (zenon_L120_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.77 apply (zenon_L121_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.77 apply (zenon_L277_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.77 apply (zenon_L389_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.77 apply (zenon_L129_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.77 apply (zenon_L278_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.77 apply (zenon_L131_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.77 apply (zenon_L164_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.77 apply (zenon_L135_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.77 apply (zenon_L136_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.77 apply (zenon_L137_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.77 apply (zenon_L138_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.77 apply (zenon_L139_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.77 apply (zenon_L140_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.77 apply (zenon_L141_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.77 apply (zenon_L142_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.77 apply (zenon_L143_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.77 apply (zenon_L144_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.77 apply (zenon_L146_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.77 apply (zenon_L147_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.77 apply (zenon_L390_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.77 apply (zenon_L151_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.77 apply (zenon_L152_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.77 apply (zenon_L153_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.77 apply (zenon_L355_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.77 apply (zenon_L356_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H35. zenon_intro zenon_H1e7. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_Hf4. zenon_intro zenon_H1d6. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H195. zenon_intro zenon_H98. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.54/8.77 apply (zenon_L1_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.54/8.77 apply (zenon_L82_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.54/8.77 apply (zenon_L83_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.54/8.77 apply (zenon_L79_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.54/8.77 apply (zenon_L80_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.54/8.77 apply (zenon_L393_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a3); [ zenon_intro zenon_H274 | zenon_intro zenon_H2b2 ]. % 8.54/8.77 apply (zenon_L244_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H2b3 ]. % 8.54/8.77 apply (zenon_L247_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H196 | zenon_intro zenon_H1b1 ]. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.54/8.77 apply (zenon_L394_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.54/8.77 apply (zenon_L263_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.54/8.77 apply (zenon_L405_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H24 | zenon_intro zenon_H301 ]. % 8.54/8.77 apply (zenon_L72_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H71 | zenon_intro zenon_H302 ]. % 8.54/8.77 apply (zenon_L19_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H7e | zenon_intro zenon_H276 ]. % 8.54/8.77 apply (zenon_L392_); trivial. % 8.54/8.77 apply (zenon_L399_); trivial. % 8.54/8.77 apply (zenon_L375_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.54/8.77 apply (zenon_L313_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.54/8.77 apply (zenon_L404_); trivial. % 8.54/8.77 apply (zenon_L246_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.77 apply (zenon_L357_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.77 apply (zenon_L186_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.77 apply (zenon_L360_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.77 apply (zenon_L188_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.77 apply (zenon_L406_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.77 apply (zenon_L316_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.77 apply (zenon_L317_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.77 apply (zenon_L364_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.77 apply (zenon_L279_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.77 apply (zenon_L241_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.77 apply (zenon_L242_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.77 apply (zenon_L366_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.77 apply (zenon_L272_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.77 apply (zenon_L407_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.77 apply (zenon_L367_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.77 apply (zenon_L369_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.77 apply (zenon_L370_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.77 apply (zenon_L274_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.77 apply (zenon_L281_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.77 apply (zenon_L276_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.77 apply (zenon_L373_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.77 apply (zenon_L374_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.77 apply (zenon_L408_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.77 apply (zenon_L377_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.77 apply (zenon_L378_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H98. zenon_intro zenon_H21e. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H21e). zenon_intro zenon_H195. zenon_intro zenon_H19f. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H19f). zenon_intro zenon_H7e. zenon_intro zenon_Hc8. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.54/8.77 apply (zenon_L393_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.54/8.77 apply (zenon_L77_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.54/8.77 apply (zenon_L23_); trivial. % 8.54/8.77 apply (zenon_L246_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.77 apply (zenon_L380_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.77 apply (zenon_L381_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.77 apply (zenon_L382_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.77 apply (zenon_L383_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.77 apply (zenon_L386_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.77 apply (zenon_L387_); trivial. % 8.54/8.77 apply (zenon_L388_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H4c. zenon_intro zenon_H57. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.77 apply (zenon_L113_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.77 apply (zenon_L114_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.77 apply (zenon_L282_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.77 apply (zenon_L118_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.77 apply (zenon_L120_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.77 apply (zenon_L121_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.77 apply (zenon_L283_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H1d1). zenon_intro zenon_H1d. zenon_intro zenon_H1d2. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H1d2). zenon_intro zenon_Hac. zenon_intro zenon_H1c7. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_H24 | zenon_intro zenon_Hc6 ]. % 8.54/8.77 apply (zenon_L310_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Had | zenon_intro zenon_Hc7 ]. % 8.54/8.77 apply (zenon_L33_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H80 | zenon_intro zenon_Hc3 ]. % 8.54/8.77 apply (zenon_L102_); trivial. % 8.54/8.77 apply (zenon_L42_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.77 apply (zenon_L129_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.77 apply (zenon_L284_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.77 apply (zenon_L131_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.77 apply (zenon_L285_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.77 apply (zenon_L135_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.77 apply (zenon_L136_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.77 apply (zenon_L410_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.77 apply (zenon_L138_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.77 apply (zenon_L139_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.77 apply (zenon_L140_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.77 apply (zenon_L286_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.77 apply (zenon_L142_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.77 apply (zenon_L143_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.77 apply (zenon_L144_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.77 apply (zenon_L146_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.77 apply (zenon_L147_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.77 apply (zenon_L411_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.77 apply (zenon_L151_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.77 apply (zenon_L152_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.77 apply (zenon_L287_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.77 apply (zenon_L355_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.77 apply (zenon_L356_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.77 apply (zenon_L412_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.77 apply (zenon_L357_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.77 apply (zenon_L186_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.77 apply (zenon_L360_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.77 apply (zenon_L188_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.77 apply (zenon_L406_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.77 apply (zenon_L316_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.77 apply (zenon_L362_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.77 apply (zenon_L364_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.77 apply (zenon_L365_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.77 apply (zenon_L241_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.77 apply (zenon_L242_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.77 apply (zenon_L366_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.77 apply (zenon_L272_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.77 apply (zenon_L407_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.77 apply (zenon_L367_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.77 apply (zenon_L369_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.77 apply (zenon_L370_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.77 apply (zenon_L274_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.77 apply (zenon_L413_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.77 apply (zenon_L293_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.77 apply (zenon_L373_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.77 apply (zenon_L374_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.77 apply (zenon_L376_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.77 apply (zenon_L414_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.77 apply (zenon_L378_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.77 apply (zenon_L415_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.77 apply (zenon_L380_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.77 apply (zenon_L381_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.77 apply (zenon_L382_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.77 apply (zenon_L383_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.77 apply (zenon_L386_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.77 apply (zenon_L387_); trivial. % 8.54/8.77 apply (zenon_L388_); trivial. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H59. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.54/8.77 apply (zenon_L113_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.54/8.77 apply (zenon_L114_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.54/8.77 apply (zenon_L116_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.54/8.77 apply (zenon_L417_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.54/8.77 apply (zenon_L120_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.54/8.77 apply (zenon_L121_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.54/8.77 apply (zenon_L122_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.54/8.77 apply (zenon_L333_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.54/8.77 apply (zenon_L129_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.54/8.77 apply (zenon_L130_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.54/8.77 apply (zenon_L131_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.54/8.77 apply (zenon_L164_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.54/8.77 apply (zenon_L135_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.54/8.77 apply (zenon_L136_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.54/8.77 apply (zenon_L418_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.54/8.77 apply (zenon_L138_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.54/8.77 apply (zenon_L139_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.54/8.77 apply (zenon_L140_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.54/8.77 apply (zenon_L141_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.54/8.77 apply (zenon_L419_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.54/8.77 apply (zenon_L143_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.54/8.77 apply (zenon_L144_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.54/8.77 apply (zenon_L146_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.54/8.77 apply (zenon_L147_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_H29. zenon_intro zenon_H1c9. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H1c9). zenon_intro zenon_H15a. zenon_intro zenon_H19f. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H19f). zenon_intro zenon_H7e. zenon_intro zenon_Hc8. % 8.54/8.77 apply (zenon_L420_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.54/8.77 apply (zenon_L151_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.54/8.77 apply (zenon_L152_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.54/8.77 apply (zenon_L297_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.54/8.77 apply (zenon_L298_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.54/8.77 apply (zenon_L356_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.54/8.77 apply (zenon_L421_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.54/8.77 apply (zenon_L357_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.54/8.77 apply (zenon_L186_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.54/8.77 apply (zenon_L360_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.54/8.77 apply (zenon_L188_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.54/8.77 apply (zenon_L422_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.54/8.77 apply (zenon_L316_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.54/8.77 apply (zenon_L317_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.54/8.77 apply (zenon_L364_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.54/8.77 apply (zenon_L335_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.54/8.77 apply (zenon_L241_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.54/8.77 apply (zenon_L242_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.54/8.77 apply (zenon_L366_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.54/8.77 apply (zenon_L299_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.54/8.77 apply (zenon_L300_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.54/8.77 apply (zenon_L423_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.54/8.77 apply (zenon_L369_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.54/8.77 apply (zenon_L370_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.54/8.77 apply (zenon_L274_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.54/8.77 apply (zenon_L413_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.54/8.77 apply (zenon_L425_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.54/8.77 apply (zenon_L373_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.54/8.77 apply (zenon_L374_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.54/8.77 apply (zenon_L408_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.54/8.77 apply (zenon_L377_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.54/8.77 apply (zenon_L378_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H98. zenon_intro zenon_H21e. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H21e). zenon_intro zenon_H195. zenon_intro zenon_H19f. % 8.54/8.77 apply (zenon_and_s _ _ zenon_H19f). zenon_intro zenon_H7e. zenon_intro zenon_Hc8. % 8.54/8.77 apply (zenon_L420_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.54/8.77 apply (zenon_L380_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.54/8.77 apply (zenon_L381_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.54/8.77 apply (zenon_L382_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.54/8.77 apply (zenon_L383_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.54/8.77 apply (zenon_L386_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.54/8.77 apply (zenon_L387_); trivial. % 8.54/8.77 apply (zenon_L388_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.54/8.77 apply (zenon_L75_); trivial. % 8.54/8.77 apply (zenon_L53_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2f4); [ zenon_intro zenon_H2a | zenon_intro zenon_H2f5 ]. % 8.54/8.77 apply (zenon_L494_); trivial. % 8.54/8.77 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1b1 ]. % 8.54/8.77 apply (zenon_L125_); trivial. % 8.54/8.77 apply (zenon_L484_); trivial. % 8.54/8.77 (* end of lemma zenon_L495_ *) % 8.54/8.77 assert (zenon_L496_ : ((op (e0) (e0)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (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) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op 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(e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (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 (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H1e zenon_H98 zenon_H71 zenon_H2a zenon_H9f zenon_H9a zenon_H3c zenon_H1d9 zenon_H173 zenon_H22d zenon_H1d7 zenon_Ha8 zenon_H192 zenon_Ha3 zenon_H2b8 zenon_H67 zenon_H197 zenon_H2b zenon_Hab zenon_Hc2 zenon_H1f6 zenon_H78 zenon_H127 zenon_H31 zenon_H25 zenon_H22e zenon_H153 zenon_H170 zenon_Hc5 zenon_H3a zenon_H2a2 zenon_H29f zenon_H2d2 zenon_H2d4 zenon_H145 zenon_H10c zenon_Hb4 zenon_H32e zenon_H109 zenon_He7 zenon_Hff zenon_H2d8 zenon_H329 zenon_H2a5 zenon_H129 zenon_H12b zenon_H2fc zenon_H36 zenon_H11f zenon_H124 zenon_H2bf zenon_H2e2 zenon_H1dd zenon_H164 zenon_Hf8 zenon_H2a3 zenon_Hf9 zenon_Hf3 zenon_H285 zenon_H2e8 zenon_H27f zenon_H137 zenon_H282 zenon_H150 zenon_H74 zenon_H6c zenon_Hb7 zenon_H2c9 zenon_H19a zenon_H295 zenon_H2a1 zenon_H1dc zenon_H169 zenon_H2c0 zenon_H2b5 zenon_H2a4 zenon_H270 zenon_H1f zenon_H16d zenon_Hd0 zenon_H2f3 zenon_H2df zenon_H1d3 zenon_H105 zenon_H322 zenon_He4 zenon_Hbf zenon_H303 zenon_Hba zenon_H331 zenon_H11e zenon_Heb zenon_H94 zenon_H336 zenon_H134 zenon_H2f8 zenon_H300 zenon_H90 zenon_Hf0 zenon_H7d. % 8.54/8.78 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.54/8.78 apply (zenon_L21_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.54/8.78 apply (zenon_L43_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.54/8.78 apply (zenon_L495_); trivial. % 8.54/8.78 apply (zenon_L55_); trivial. % 8.54/8.78 (* end of lemma zenon_L496_ *) % 8.54/8.78 assert (zenon_L497_ : ((op (e0) (e0)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (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 (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H1e zenon_H98 zenon_H3c zenon_Hd6 zenon_Hed zenon_H1d9 zenon_H173 zenon_H22d zenon_H1d7 zenon_Ha8 zenon_H192 zenon_Ha3 zenon_H2b8 zenon_H67 zenon_H197 zenon_H2b zenon_Hab zenon_Hc2 zenon_H1f6 zenon_H78 zenon_H127 zenon_H31 zenon_H25 zenon_H22e zenon_H153 zenon_H170 zenon_Hc5 zenon_H3a zenon_H2a2 zenon_H29f zenon_H2d2 zenon_H2d4 zenon_H145 zenon_H10c zenon_Hb4 zenon_H32e zenon_H109 zenon_He7 zenon_Hff zenon_H2d8 zenon_H329 zenon_H2a5 zenon_H129 zenon_H12b zenon_H2fc zenon_H36 zenon_H11f zenon_H124 zenon_H2bf zenon_H2e2 zenon_H1dd zenon_H164 zenon_Hf8 zenon_H2a3 zenon_Hf9 zenon_Hf3 zenon_H285 zenon_H2e8 zenon_H27f zenon_H137 zenon_H282 zenon_H150 zenon_H74 zenon_H6c zenon_Hb7 zenon_H2c9 zenon_H19a zenon_H295 zenon_H2a1 zenon_H1dc zenon_H169 zenon_H2c0 zenon_H2b5 zenon_H2a4 zenon_H270 zenon_H1f zenon_H16d zenon_Hd0 zenon_H2f3 zenon_H2df zenon_H1d3 zenon_H105 zenon_H322 zenon_He4 zenon_Hbf zenon_H303 zenon_Hba zenon_H331 zenon_H11e zenon_Heb zenon_H94 zenon_H336 zenon_H134 zenon_H2f8 zenon_H300 zenon_H90 zenon_Hf0 zenon_H7d. % 8.54/8.78 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.54/8.78 apply (zenon_L21_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.54/8.78 apply (zenon_L54_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.54/8.78 apply (zenon_L495_); trivial. % 8.54/8.78 apply (zenon_L55_); trivial. % 8.54/8.78 (* end of lemma zenon_L497_ *) % 8.54/8.78 assert (zenon_L498_ : ((op (e1) (e1)) = (e1)) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op 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(e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (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 (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H2a zenon_H1e zenon_H98 zenon_H3c zenon_Hd6 zenon_Hed zenon_H1d9 zenon_H173 zenon_H22d zenon_H1d7 zenon_Ha8 zenon_H192 zenon_Ha3 zenon_H2b8 zenon_H67 zenon_H197 zenon_H2b zenon_Hab zenon_Hc2 zenon_H1f6 zenon_H78 zenon_H127 zenon_H31 zenon_H25 zenon_H22e zenon_H153 zenon_H170 zenon_Hc5 zenon_H3a zenon_H2a2 zenon_H29f zenon_H2d2 zenon_H2d4 zenon_H145 zenon_H10c zenon_Hb4 zenon_H32e zenon_H109 zenon_He7 zenon_Hff zenon_H2d8 zenon_H329 zenon_H2a5 zenon_H129 zenon_H12b zenon_H2fc zenon_H36 zenon_H11f zenon_H124 zenon_H2bf zenon_H2e2 zenon_H1dd zenon_H164 zenon_Hf8 zenon_H2a3 zenon_Hf9 zenon_Hf3 zenon_H285 zenon_H2e8 zenon_H27f zenon_H137 zenon_H282 zenon_H150 zenon_H74 zenon_H6c zenon_Hb7 zenon_H2c9 zenon_H19a zenon_H295 zenon_H2a1 zenon_H1dc zenon_H169 zenon_H2c0 zenon_H2b5 zenon_H2a4 zenon_H270 zenon_H1f zenon_H16d zenon_Hd0 zenon_H2f3 zenon_H2df zenon_H1d3 zenon_H105 zenon_H322 zenon_He4 zenon_Hbf zenon_H303 zenon_Hba zenon_H331 zenon_H11e zenon_Heb zenon_H94 zenon_H336 zenon_H134 zenon_H2f8 zenon_H300 zenon_H90 zenon_H7d. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.54/8.78 apply (zenon_L87_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.54/8.78 apply (zenon_L20_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.54/8.78 apply (zenon_L58_); trivial. % 8.54/8.78 apply (zenon_L497_); trivial. % 8.54/8.78 (* end of lemma zenon_L498_ *) % 8.54/8.78 assert (zenon_L499_ : (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e0)) -> False). % 8.54/8.78 do 0 intro. intros zenon_H67 zenon_H73 zenon_Hac. % 8.54/8.78 cut (((op (e1) (e0)) = (e1)) = ((e0) = (e1))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H67. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_H73. % 8.54/8.78 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.54/8.78 cut (((op (e1) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H142]. % 8.54/8.78 congruence. % 8.54/8.78 exact (zenon_H142 zenon_Hac). % 8.54/8.78 apply zenon_H40. apply refl_equal. % 8.54/8.78 (* end of lemma zenon_L499_ *) % 8.54/8.78 assert (zenon_L500_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 8.54/8.78 do 0 intro. intros zenon_H109 zenon_Hd1 zenon_H10f. % 8.54/8.78 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H109. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_Hd1. % 8.54/8.78 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 8.54/8.78 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 8.54/8.78 congruence. % 8.54/8.78 apply zenon_H38. apply refl_equal. % 8.54/8.78 apply zenon_H14d. apply sym_equal. exact zenon_H10f. % 8.54/8.78 (* end of lemma zenon_L500_ *) % 8.54/8.78 assert (zenon_L501_ : ((op (e3) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H5a zenon_H195 zenon_He7. % 8.54/8.78 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 8.54/8.78 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_He7. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_H149. % 8.54/8.78 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 8.54/8.78 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H339]. % 8.54/8.78 congruence. % 8.54/8.78 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H339. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_H5a. % 8.54/8.78 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2d7]. % 8.54/8.78 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 8.54/8.78 congruence. % 8.54/8.78 apply zenon_H14a. apply refl_equal. % 8.54/8.78 apply zenon_H2d7. apply sym_equal. exact zenon_H195. % 8.54/8.78 apply zenon_H14a. apply refl_equal. % 8.54/8.78 apply zenon_H14a. apply refl_equal. % 8.54/8.78 (* end of lemma zenon_L501_ *) % 8.54/8.78 assert (zenon_L502_ : (((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 (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H2d8 zenon_Hd1 zenon_H109 zenon_H15a zenon_H197 zenon_H3b zenon_H3a zenon_H5a zenon_He7. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H2d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H2d9 ]. % 8.54/8.78 apply (zenon_L500_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H2d9); [ zenon_intro zenon_H16b | zenon_intro zenon_H2da ]. % 8.54/8.78 apply (zenon_L472_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H3c | zenon_intro zenon_H195 ]. % 8.54/8.78 apply (zenon_L6_); trivial. % 8.54/8.78 apply (zenon_L501_); trivial. % 8.54/8.78 (* end of lemma zenon_L502_ *) % 8.54/8.78 assert (zenon_L503_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H105 zenon_Hd4 zenon_H16b zenon_Hff zenon_H108 zenon_Hd0 zenon_H5a zenon_He4. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H30 | zenon_intro zenon_H106 ]. % 8.54/8.78 apply (zenon_L66_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H107 ]. % 8.54/8.78 apply (zenon_L107_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfe | zenon_intro zenon_H103 ]. % 8.54/8.78 apply (zenon_L88_); trivial. % 8.54/8.78 apply (zenon_L89_); trivial. % 8.54/8.78 (* end of lemma zenon_L503_ *) % 8.54/8.78 assert (zenon_L504_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H2d8 zenon_H143 zenon_H12b zenon_He4 zenon_Hd0 zenon_H108 zenon_Hff zenon_Hd4 zenon_H105 zenon_H3b zenon_H3a zenon_H5a zenon_He7. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H2d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H2d9 ]. % 8.54/8.78 apply (zenon_L253_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H2d9); [ zenon_intro zenon_H16b | zenon_intro zenon_H2da ]. % 8.54/8.78 apply (zenon_L503_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H3c | zenon_intro zenon_H195 ]. % 8.54/8.78 apply (zenon_L6_); trivial. % 8.54/8.78 apply (zenon_L501_); trivial. % 8.54/8.78 (* end of lemma zenon_L504_ *) % 8.54/8.78 assert (zenon_L505_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 8.54/8.78 do 0 intro. intros zenon_H329 zenon_H7d zenon_Hd6 zenon_He7 zenon_H105 zenon_Hd4 zenon_Hff zenon_Hd0 zenon_He4 zenon_H12b zenon_H143 zenon_H2d8 zenon_H3b zenon_H3a zenon_Ha8 zenon_H5a. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hfe | zenon_intro zenon_H32a ]. % 8.54/8.78 apply (zenon_L81_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H108 | zenon_intro zenon_H32b ]. % 8.54/8.78 apply (zenon_L504_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H3c | zenon_intro zenon_He8 ]. % 8.54/8.78 apply (zenon_L6_); trivial. % 8.54/8.78 apply (zenon_L439_); trivial. % 8.54/8.78 (* end of lemma zenon_L505_ *) % 8.54/8.78 assert (zenon_L506_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (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). % 8.54/8.78 do 0 intro. intros zenon_H2b5 zenon_H197 zenon_H15a zenon_H109 zenon_He5 zenon_He7 zenon_H3a zenon_H3b zenon_H105 zenon_Hd4 zenon_Hff zenon_Hd0 zenon_He4 zenon_H12b zenon_H143 zenon_H2d8 zenon_H5a zenon_H16d. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H2b6 ]. % 8.54/8.78 apply (zenon_L502_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H35 | zenon_intro zenon_H2b7 ]. % 8.54/8.78 apply (zenon_L267_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H108 | zenon_intro zenon_Hb3 ]. % 8.54/8.78 apply (zenon_L504_); trivial. % 8.54/8.78 apply (zenon_L109_); trivial. % 8.54/8.78 (* end of lemma zenon_L506_ *) % 8.54/8.78 assert (zenon_L507_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (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). % 8.54/8.78 do 0 intro. intros zenon_H2b8 zenon_Ha8 zenon_H7d zenon_H329 zenon_Hb4 zenon_H73 zenon_H2b5 zenon_H197 zenon_H15a zenon_H109 zenon_He7 zenon_H3a zenon_H3b zenon_H105 zenon_Hd4 zenon_Hff zenon_Hd0 zenon_He4 zenon_H12b zenon_H143 zenon_H2d8 zenon_H5a zenon_H16d. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H2b9 ]. % 8.54/8.78 apply (zenon_L505_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_H35 | zenon_intro zenon_H2ba ]. % 8.54/8.78 apply (zenon_L119_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H16b | zenon_intro zenon_He5 ]. % 8.54/8.78 apply (zenon_L472_); trivial. % 8.54/8.78 apply (zenon_L506_); trivial. % 8.54/8.78 (* end of lemma zenon_L507_ *) % 8.54/8.78 assert (zenon_L508_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H73 zenon_Hb0 zenon_H7d. % 8.54/8.78 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H79 | zenon_intro zenon_H4b ]. % 8.54/8.78 cut (((e2) = (e2)) = ((e1) = (e2))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H7d. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_H79. % 8.54/8.78 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.54/8.78 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hce]. % 8.54/8.78 congruence. % 8.54/8.78 cut (((op (e1) (e0)) = (e1)) = ((e2) = (e1))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_Hce. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_H73. % 8.54/8.78 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.54/8.78 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2c8]. % 8.54/8.78 congruence. % 8.54/8.78 exact (zenon_H2c8 zenon_Hb0). % 8.54/8.78 apply zenon_H40. apply refl_equal. % 8.54/8.78 apply zenon_H4b. apply refl_equal. % 8.54/8.78 apply zenon_H4b. apply refl_equal. % 8.54/8.78 (* end of lemma zenon_L508_ *) % 8.54/8.78 assert (zenon_L509_ : ((op (e2) (e1)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H191 zenon_Hcc zenon_H2c9. % 8.54/8.78 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H193 | zenon_intro zenon_H16a ]. % 8.54/8.78 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e1) (e1)) = (op (e2) (e1)))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H2c9. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_H193. % 8.54/8.78 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 8.54/8.78 cut (((op (e2) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H33a]. % 8.54/8.78 congruence. % 8.54/8.78 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e1) (e1)))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H33a. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_H191. % 8.54/8.78 cut (((e2) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hcd]. % 8.54/8.78 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 8.54/8.78 congruence. % 8.54/8.78 apply zenon_H16a. apply refl_equal. % 8.54/8.78 apply zenon_Hcd. apply sym_equal. exact zenon_Hcc. % 8.54/8.78 apply zenon_H16a. apply refl_equal. % 8.54/8.78 apply zenon_H16a. apply refl_equal. % 8.54/8.78 (* end of lemma zenon_L509_ *) % 8.54/8.78 assert (zenon_L510_ : (~((op (op (e1) (e1)) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> False). % 8.54/8.78 do 0 intro. intros zenon_H33b zenon_Hcc. % 8.54/8.78 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.54/8.78 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 8.54/8.78 congruence. % 8.54/8.78 exact (zenon_Hcf zenon_Hcc). % 8.54/8.78 apply zenon_H40. apply refl_equal. % 8.54/8.78 (* end of lemma zenon_L510_ *) % 8.54/8.78 assert (zenon_L511_ : ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((e3) = (op (op (e1) (e1)) (e1)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H196 zenon_Hcc zenon_H33c. % 8.54/8.78 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H33d | zenon_intro zenon_H33e ]. % 8.54/8.78 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e3) = (op (op (e1) (e1)) (e1)))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H33c. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_H33d. % 8.54/8.78 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H33e]. % 8.54/8.78 cut (((op (op (e1) (e1)) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H33f]. % 8.54/8.78 congruence. % 8.54/8.78 cut (((op (e2) (e1)) = (e3)) = ((op (op (e1) (e1)) (e1)) = (e3))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H33f. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_H196. % 8.54/8.78 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.78 cut (((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H340]. % 8.54/8.78 congruence. % 8.54/8.78 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H33d | zenon_intro zenon_H33e ]. % 8.54/8.78 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H340. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_H33d. % 8.54/8.78 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H33e]. % 8.54/8.78 cut (((op (op (e1) (e1)) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H33b]. % 8.54/8.78 congruence. % 8.54/8.78 apply (zenon_L510_); trivial. % 8.54/8.78 apply zenon_H33e. apply refl_equal. % 8.54/8.78 apply zenon_H33e. apply refl_equal. % 8.54/8.78 apply zenon_H58. apply refl_equal. % 8.54/8.78 apply zenon_H33e. apply refl_equal. % 8.54/8.78 apply zenon_H33e. apply refl_equal. % 8.54/8.78 (* end of lemma zenon_L511_ *) % 8.54/8.78 assert (zenon_L512_ : ((op (e3) (e2)) = (e0)) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> False). % 8.54/8.78 do 0 intro. intros zenon_Hc3 zenon_H196 zenon_Hcc. % 8.54/8.78 apply (zenon_notand_s _ _ ax20); [ zenon_intro zenon_Hcd | zenon_intro zenon_H341 ]. % 8.54/8.78 apply zenon_Hcd. apply sym_equal. exact zenon_Hcc. % 8.54/8.78 apply (zenon_notand_s _ _ zenon_H341); [ zenon_intro zenon_H342 | zenon_intro zenon_H33c ]. % 8.54/8.78 elim (classic ((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H343 | zenon_intro zenon_H344 ]. % 8.54/8.78 cut (((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1)))) = ((e0) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H342. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_H343. % 8.54/8.78 cut (((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H344]. % 8.54/8.78 cut (((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H345]. % 8.54/8.78 congruence. % 8.54/8.78 cut (((op (e3) (e2)) = (e0)) = ((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (e0))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H345. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_Hc3. % 8.54/8.78 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.54/8.78 cut (((op (e3) (e2)) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H346]. % 8.54/8.78 congruence. % 8.54/8.78 elim (classic ((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H343 | zenon_intro zenon_H344 ]. % 8.54/8.78 cut (((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1)))) = ((op (e3) (e2)) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H346. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_H343. % 8.54/8.78 cut (((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H344]. % 8.54/8.78 cut (((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H347]. % 8.54/8.78 congruence. % 8.54/8.78 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 8.54/8.78 cut (((op (op (e1) (e1)) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H33f]. % 8.54/8.78 congruence. % 8.54/8.78 cut (((op (e2) (e1)) = (e3)) = ((op (op (e1) (e1)) (e1)) = (e3))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H33f. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_H196. % 8.54/8.78 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.54/8.78 cut (((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H340]. % 8.54/8.78 congruence. % 8.54/8.78 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H33d | zenon_intro zenon_H33e ]. % 8.54/8.78 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H340. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_H33d. % 8.54/8.78 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H33e]. % 8.54/8.78 cut (((op (op (e1) (e1)) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H33b]. % 8.54/8.78 congruence. % 8.54/8.78 apply (zenon_L510_); trivial. % 8.54/8.78 apply zenon_H33e. apply refl_equal. % 8.54/8.78 apply zenon_H33e. apply refl_equal. % 8.54/8.78 apply zenon_H58. apply refl_equal. % 8.54/8.78 exact (zenon_Hcf zenon_Hcc). % 8.54/8.78 apply zenon_H344. apply refl_equal. % 8.54/8.78 apply zenon_H344. apply refl_equal. % 8.54/8.78 apply zenon_H3f. apply refl_equal. % 8.54/8.78 apply zenon_H344. apply refl_equal. % 8.54/8.78 apply zenon_H344. apply refl_equal. % 8.54/8.78 apply (zenon_L511_); trivial. % 8.54/8.78 (* end of lemma zenon_L512_ *) % 8.54/8.78 assert (zenon_L513_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 8.54/8.78 do 0 intro. intros zenon_H9a zenon_H3b zenon_Hbd. % 8.54/8.78 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H9a. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_H3b. % 8.54/8.78 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d3]. % 8.54/8.78 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 8.54/8.78 congruence. % 8.54/8.78 apply zenon_H3e. apply refl_equal. % 8.54/8.78 apply zenon_H2d3. apply sym_equal. exact zenon_Hbd. % 8.54/8.78 (* end of lemma zenon_L513_ *) % 8.54/8.78 assert (zenon_L514_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((e0) = (e1))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H181 zenon_H67. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H181). zenon_intro zenon_H1d. zenon_intro zenon_H182. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H182). zenon_intro zenon_Hac. zenon_intro zenon_H183. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H183). zenon_intro zenon_H6b. zenon_intro zenon_H73. % 8.54/8.78 apply (zenon_L77_); trivial. % 8.54/8.78 (* end of lemma zenon_L514_ *) % 8.54/8.78 assert (zenon_L515_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H184 zenon_H73 zenon_H74. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H184). zenon_intro zenon_H1d. zenon_intro zenon_H185. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H185). zenon_intro zenon_Hac. zenon_intro zenon_H186. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H186). zenon_intro zenon_H2a. zenon_intro zenon_H2a. % 8.54/8.78 apply (zenon_L20_); trivial. % 8.54/8.78 (* end of lemma zenon_L515_ *) % 8.54/8.78 assert (zenon_L516_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H187 zenon_H73 zenon_Hab. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H187). zenon_intro zenon_H1d. zenon_intro zenon_H188. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H188). zenon_intro zenon_Hac. zenon_intro zenon_H189. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H15a. zenon_intro zenon_H29. % 8.54/8.78 apply (zenon_L93_); trivial. % 8.54/8.78 (* end of lemma zenon_L516_ *) % 8.54/8.78 assert (zenon_L517_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H1d1 zenon_H73 zenon_Hb4. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1d1). zenon_intro zenon_H1d. zenon_intro zenon_H1d2. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1d2). zenon_intro zenon_Hac. zenon_intro zenon_H1c7. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_Hf4. zenon_intro zenon_H35. % 8.54/8.78 apply (zenon_L119_); trivial. % 8.54/8.78 (* end of lemma zenon_L517_ *) % 8.54/8.78 assert (zenon_L518_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> False). % 8.54/8.78 do 0 intro. intros zenon_H1a0 zenon_H197 zenon_H3c. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1a0). zenon_intro zenon_H24. zenon_intro zenon_H1a1. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1a1). zenon_intro zenon_H143. zenon_intro zenon_H1a2. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1a2). zenon_intro zenon_H93. zenon_intro zenon_H191. % 8.54/8.78 apply (zenon_L191_); trivial. % 8.54/8.78 (* end of lemma zenon_L518_ *) % 8.54/8.78 assert (zenon_L519_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.54/8.78 do 0 intro. intros zenon_H1ae zenon_H1d9 zenon_H98. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_H30. zenon_intro zenon_H1af. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_H14e. zenon_intro zenon_H1b0. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb3. zenon_intro zenon_H1b1. % 8.54/8.78 apply (zenon_L375_); trivial. % 8.54/8.78 (* end of lemma zenon_L519_ *) % 8.54/8.78 assert (zenon_L520_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((e0) = (e1))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H1b9 zenon_H67. % 8.54/8.78 apply (zenon_L140_); trivial. % 8.54/8.78 (* end of lemma zenon_L520_ *) % 8.54/8.78 assert (zenon_L521_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H1bb zenon_H1d zenon_H124. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1bb). zenon_intro zenon_H73. zenon_intro zenon_H1bc. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1bc). zenon_intro zenon_H6b. zenon_intro zenon_H17d. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H143. zenon_intro zenon_H24. % 8.54/8.78 apply (zenon_L72_); trivial. % 8.54/8.78 (* end of lemma zenon_L521_ *) % 8.54/8.78 assert (zenon_L522_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H1bf zenon_H6c. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1bf). zenon_intro zenon_H2a. zenon_intro zenon_H1c0. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1c0). zenon_intro zenon_H2a. zenon_intro zenon_H183. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H183). zenon_intro zenon_H6b. zenon_intro zenon_H73. % 8.54/8.78 apply (zenon_L18_); trivial. % 8.54/8.78 (* end of lemma zenon_L522_ *) % 8.54/8.78 assert (zenon_L523_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H1c1 zenon_H73 zenon_H74. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1c1). zenon_intro zenon_H2a. zenon_intro zenon_H1c2. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1c2). zenon_intro zenon_H2a. zenon_intro zenon_H186. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H186). zenon_intro zenon_H2a. zenon_intro zenon_H2a. % 8.54/8.78 apply (zenon_L20_); trivial. % 8.54/8.78 (* end of lemma zenon_L523_ *) % 8.54/8.78 assert (zenon_L524_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H1c5 zenon_H36. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1c5). zenon_intro zenon_H2a. zenon_intro zenon_H1c6. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1c6). zenon_intro zenon_H2a. zenon_intro zenon_H1c7. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_Hf4. zenon_intro zenon_H35. % 8.54/8.78 apply (zenon_L5_); trivial. % 8.54/8.78 (* end of lemma zenon_L524_ *) % 8.54/8.78 assert (zenon_L525_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H1ce zenon_H73 zenon_Hab. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H29. zenon_intro zenon_H1cf. % 8.54/8.78 apply (zenon_L93_); trivial. % 8.54/8.78 (* end of lemma zenon_L525_ *) % 8.54/8.78 assert (zenon_L526_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H1e6 zenon_H73 zenon_Hb4. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H35. zenon_intro zenon_H1e7. % 8.54/8.78 apply (zenon_L119_); trivial. % 8.54/8.78 (* end of lemma zenon_L526_ *) % 8.54/8.78 assert (zenon_L527_ : (~((op (e0) (op (e0) (e1))) = (e1))) -> ((op (e0) (e1)) = (e1)) -> False). % 8.54/8.78 do 0 intro. intros zenon_H2aa zenon_H6b. % 8.54/8.78 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (op (e0) (e1))) = (e1))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H2aa. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_H6b. % 8.54/8.78 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.54/8.78 cut (((op (e0) (e1)) = (op (e0) (op (e0) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H348]. % 8.54/8.78 congruence. % 8.54/8.78 elim (classic ((op (e0) (op (e0) (e1))) = (op (e0) (op (e0) (e1))))); [ zenon_intro zenon_H349 | zenon_intro zenon_H34a ]. % 8.54/8.78 cut (((op (e0) (op (e0) (e1))) = (op (e0) (op (e0) (e1)))) = ((op (e0) (e1)) = (op (e0) (op (e0) (e1))))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H348. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_H349. % 8.54/8.78 cut (((op (e0) (op (e0) (e1))) = (op (e0) (op (e0) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H34a]. % 8.54/8.78 cut (((op (e0) (op (e0) (e1))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H34b]. % 8.54/8.78 congruence. % 8.54/8.78 cut (((op (e0) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 8.54/8.78 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.54/8.78 congruence. % 8.54/8.78 apply zenon_H3f. apply refl_equal. % 8.54/8.78 exact (zenon_H133 zenon_H6b). % 8.54/8.78 apply zenon_H34a. apply refl_equal. % 8.54/8.78 apply zenon_H34a. apply refl_equal. % 8.54/8.78 apply zenon_H40. apply refl_equal. % 8.54/8.78 (* end of lemma zenon_L527_ *) % 8.54/8.78 assert (zenon_L528_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e0) (op (e0) (e1))) = (e1))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H1f2 zenon_H2aa. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1f2). zenon_intro zenon_H191. zenon_intro zenon_H1f3. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H93. zenon_intro zenon_H183. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H183). zenon_intro zenon_H6b. zenon_intro zenon_H73. % 8.54/8.78 apply (zenon_L527_); trivial. % 8.54/8.78 (* end of lemma zenon_L528_ *) % 8.54/8.78 assert (zenon_L529_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H1f4 zenon_H73 zenon_H74. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1f4). zenon_intro zenon_H191. zenon_intro zenon_H1f5. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1f5). zenon_intro zenon_H93. zenon_intro zenon_H186. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H186). zenon_intro zenon_H2a. zenon_intro zenon_H2a. % 8.54/8.78 apply (zenon_L20_); trivial. % 8.54/8.78 (* end of lemma zenon_L529_ *) % 8.54/8.78 assert (zenon_L530_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H1fb zenon_H73 zenon_Hb4. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H191. zenon_intro zenon_H1fc. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_H93. zenon_intro zenon_H1c7. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_Hf4. zenon_intro zenon_H35. % 8.54/8.78 apply (zenon_L119_); trivial. % 8.54/8.78 (* end of lemma zenon_L530_ *) % 8.54/8.78 assert (zenon_L531_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> False). % 8.54/8.78 do 0 intro. intros zenon_H201 zenon_H3a zenon_H3c. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H201). zenon_intro zenon_H3b. zenon_intro zenon_H202. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H202). zenon_intro zenon_H3b. zenon_intro zenon_H1a5. % 8.54/8.78 apply (zenon_and_s _ _ zenon_H1a5). zenon_intro zenon_H3b. zenon_intro zenon_H3b. % 8.54/8.78 apply (zenon_L6_); trivial. % 8.54/8.78 (* end of lemma zenon_L531_ *) % 8.54/8.78 assert (zenon_L532_ : ((op (e1) (e3)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_Hb3 zenon_Ha7 zenon_H129. % 8.54/8.78 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H37 | zenon_intro zenon_H38 ]. % 8.54/8.78 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e2)) = (op (e1) (e3)))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H129. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_H37. % 8.54/8.78 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 8.54/8.78 cut (((op (e1) (e3)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H34c]. % 8.54/8.78 congruence. % 8.54/8.78 cut (((op (e1) (e3)) = (e3)) = ((op (e1) (e3)) = (op (e1) (e2)))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H34c. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_Hb3. % 8.54/8.78 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2f7]. % 8.54/8.78 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 8.54/8.78 congruence. % 8.54/8.78 apply zenon_H38. apply refl_equal. % 8.54/8.78 apply zenon_H2f7. apply sym_equal. exact zenon_Ha7. % 8.54/8.78 apply zenon_H38. apply refl_equal. % 8.54/8.78 apply zenon_H38. apply refl_equal. % 8.54/8.78 (* end of lemma zenon_L532_ *) % 8.54/8.78 assert (zenon_L533_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H2f8 zenon_H24 zenon_H134 zenon_Hab zenon_H73 zenon_Hbd zenon_H2d2 zenon_Hb3 zenon_H129. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_Had | zenon_intro zenon_H2f9 ]. % 8.54/8.78 apply (zenon_L397_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H29 | zenon_intro zenon_H2fa ]. % 8.54/8.78 apply (zenon_L93_); trivial. % 8.54/8.78 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H93 | zenon_intro zenon_Ha7 ]. % 8.54/8.78 apply (zenon_L320_); trivial. % 8.54/8.78 apply (zenon_L532_); trivial. % 8.54/8.78 (* end of lemma zenon_L533_ *) % 8.54/8.78 assert (zenon_L534_ : ((op (e2) (e1)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> False). % 8.54/8.78 do 0 intro. intros zenon_H15a zenon_H6b zenon_H164. % 8.54/8.78 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H193 | zenon_intro zenon_H16a ]. % 8.54/8.78 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e0) (e1)) = (op (e2) (e1)))). % 8.54/8.78 intro zenon_D_pnotp. % 8.54/8.78 apply zenon_H164. % 8.54/8.78 rewrite <- zenon_D_pnotp. % 8.54/8.78 exact zenon_H193. % 8.54/8.78 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 8.54/8.78 cut (((op (e2) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2ce]. % 8.54/8.78 congruence. % 8.54/8.78 cut (((op (e2) (e1)) = (e1)) = ((op (e2) (e1)) = (op (e0) (e1)))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_H2ce. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H15a. % 8.61/8.79 cut (((e1) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 8.61/8.79 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 8.61/8.79 congruence. % 8.61/8.79 apply zenon_H16a. apply refl_equal. % 8.61/8.79 apply zenon_H70. apply sym_equal. exact zenon_H6b. % 8.61/8.79 apply zenon_H16a. apply refl_equal. % 8.61/8.79 apply zenon_H16a. apply refl_equal. % 8.61/8.79 (* end of lemma zenon_L534_ *) % 8.61/8.79 assert (zenon_L535_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H19a zenon_H143 zenon_H192 zenon_H164 zenon_H6b zenon_H3c zenon_H197 zenon_H1b1 zenon_H169. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H165 | zenon_intro zenon_H19b ]. % 8.61/8.79 apply (zenon_L249_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H15a | zenon_intro zenon_H19c ]. % 8.61/8.79 apply (zenon_L534_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H191 | zenon_intro zenon_H196 ]. % 8.61/8.79 apply (zenon_L191_); trivial. % 8.61/8.79 apply (zenon_L432_); trivial. % 8.61/8.79 (* end of lemma zenon_L535_ *) % 8.61/8.79 assert (zenon_L536_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H1bb zenon_H19a zenon_H192 zenon_H164 zenon_H3c zenon_H197 zenon_H1b1 zenon_H169. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1bb). zenon_intro zenon_H73. zenon_intro zenon_H1bc. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1bc). zenon_intro zenon_H6b. zenon_intro zenon_H17d. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H143. zenon_intro zenon_H24. % 8.61/8.79 apply (zenon_L535_); trivial. % 8.61/8.79 (* end of lemma zenon_L536_ *) % 8.61/8.79 assert (zenon_L537_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H211 zenon_H2f3 zenon_Hd0 zenon_H16d zenon_H1f zenon_H270 zenon_H2a4 zenon_H2b5 zenon_H2b8 zenon_H2c0 zenon_H169 zenon_H1dc zenon_H2a1 zenon_H295 zenon_H19a zenon_H2c9 zenon_H145 zenon_Hb7 zenon_H6c zenon_Ha3 zenon_H74 zenon_H150 zenon_H282 zenon_H137 zenon_H173 zenon_H27f zenon_H10c zenon_H2e8 zenon_H285 zenon_Hf3 zenon_Hf9 zenon_H78 zenon_H2a2 zenon_H3a zenon_H170 zenon_H1f6 zenon_H22d zenon_Hc2 zenon_H192 zenon_H7d zenon_H2b zenon_Hab zenon_H31 zenon_H22e zenon_H129 zenon_H197 zenon_H1d7 zenon_H11f zenon_H67 zenon_H12b zenon_H124 zenon_H25 zenon_H36 zenon_Hb4 zenon_H153 zenon_H1d9 zenon_H2df zenon_Ha8 zenon_H127 zenon_H2a3 zenon_Hff zenon_H109 zenon_H2d8 zenon_Hf8 zenon_H164 zenon_H1dd zenon_H2e2 zenon_H2d2 zenon_H29f zenon_H2d4 zenon_H2a5 zenon_H2bf zenon_H1d3. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H211). zenon_intro zenon_H1a9. zenon_intro zenon_H212. % 8.61/8.79 apply (zenon_L354_); trivial. % 8.61/8.79 (* end of lemma zenon_L537_ *) % 8.61/8.79 assert (zenon_L538_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e0) (op (e0) (e1))) = (e1))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H215 zenon_H2aa. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H215). zenon_intro zenon_H1b1. zenon_intro zenon_H216. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H216). zenon_intro zenon_Hb3. zenon_intro zenon_H183. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H183). zenon_intro zenon_H6b. zenon_intro zenon_H73. % 8.61/8.79 apply (zenon_L527_); trivial. % 8.61/8.79 (* end of lemma zenon_L538_ *) % 8.61/8.79 assert (zenon_L539_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H217 zenon_H73 zenon_H74. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H217). zenon_intro zenon_H1b1. zenon_intro zenon_H218. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H218). zenon_intro zenon_Hb3. zenon_intro zenon_H186. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H186). zenon_intro zenon_H2a. zenon_intro zenon_H2a. % 8.61/8.79 apply (zenon_L20_); trivial. % 8.61/8.79 (* end of lemma zenon_L539_ *) % 8.61/8.79 assert (zenon_L540_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H219 zenon_H73 zenon_Hab. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H219). zenon_intro zenon_H1b1. zenon_intro zenon_H21a. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H21a). zenon_intro zenon_Hb3. zenon_intro zenon_H189. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H15a. zenon_intro zenon_H29. % 8.61/8.79 apply (zenon_L93_); trivial. % 8.61/8.79 (* end of lemma zenon_L540_ *) % 8.61/8.79 assert (zenon_L541_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H21f zenon_H197 zenon_H3c. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H21f). zenon_intro zenon_H98. zenon_intro zenon_H220. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H220). zenon_intro zenon_H195. zenon_intro zenon_H1a2. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1a2). zenon_intro zenon_H93. zenon_intro zenon_H191. % 8.61/8.79 apply (zenon_L191_); trivial. % 8.61/8.79 (* end of lemma zenon_L541_ *) % 8.61/8.79 assert (zenon_L542_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H221 zenon_H1d9 zenon_H1b1. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H221). zenon_intro zenon_H98. zenon_intro zenon_H222. % 8.61/8.79 apply (zenon_L375_); trivial. % 8.61/8.79 (* end of lemma zenon_L542_ *) % 8.61/8.79 assert (zenon_L543_ : ((op (e1) (e0)) = (e1)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H73 zenon_H66 zenon_H34d. % 8.61/8.79 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H34e | zenon_intro zenon_Haf ]. % 8.61/8.79 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e0) (e0)) = (op (e1) (e0)))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_H34d. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H34e. % 8.61/8.79 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 8.61/8.79 cut (((op (e1) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H34f]. % 8.61/8.79 congruence. % 8.61/8.79 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e0) (e0)))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_H34f. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H73. % 8.61/8.79 cut (((e1) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 8.61/8.79 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 8.61/8.79 congruence. % 8.61/8.79 apply zenon_Haf. apply refl_equal. % 8.61/8.79 apply zenon_H72. apply sym_equal. exact zenon_H66. % 8.61/8.79 apply zenon_Haf. apply refl_equal. % 8.61/8.79 apply zenon_Haf. apply refl_equal. % 8.61/8.79 (* end of lemma zenon_L543_ *) % 8.61/8.79 assert (zenon_L544_ : (~((op (e1) (op (e1) (e3))) = (e3))) -> ((op (e1) (e3)) = (e3)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H2c3 zenon_Hb3. % 8.61/8.79 cut (((op (e1) (e3)) = (e3)) = ((op (e1) (op (e1) (e3))) = (e3))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_H2c3. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_Hb3. % 8.61/8.79 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.61/8.79 cut (((op (e1) (e3)) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H350]. % 8.61/8.79 congruence. % 8.61/8.79 elim (classic ((op (e1) (op (e1) (e3))) = (op (e1) (op (e1) (e3))))); [ zenon_intro zenon_H351 | zenon_intro zenon_H352 ]. % 8.61/8.79 cut (((op (e1) (op (e1) (e3))) = (op (e1) (op (e1) (e3)))) = ((op (e1) (e3)) = (op (e1) (op (e1) (e3))))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_H350. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H351. % 8.61/8.79 cut (((op (e1) (op (e1) (e3))) = (op (e1) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H352]. % 8.61/8.79 cut (((op (e1) (op (e1) (e3))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H353]. % 8.61/8.79 congruence. % 8.61/8.79 cut (((op (e1) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 8.61/8.79 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.61/8.79 congruence. % 8.61/8.79 apply zenon_H40. apply refl_equal. % 8.61/8.79 exact (zenon_H190 zenon_Hb3). % 8.61/8.79 apply zenon_H352. apply refl_equal. % 8.61/8.79 apply zenon_H352. apply refl_equal. % 8.61/8.79 apply zenon_H58. apply refl_equal. % 8.61/8.79 (* end of lemma zenon_L544_ *) % 8.61/8.79 assert (zenon_L545_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H331 zenon_Hd6 zenon_Ha3 zenon_H2c3 zenon_Ha8 zenon_H3c zenon_H2fc zenon_H1b1. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H331); [ zenon_intro zenon_H103 | zenon_intro zenon_H332 ]. % 8.61/8.79 apply (zenon_L288_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H332); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H333 ]. % 8.61/8.79 apply (zenon_L544_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H333); [ zenon_intro zenon_H195 | zenon_intro zenon_H5a ]. % 8.61/8.79 apply (zenon_L368_); trivial. % 8.61/8.79 apply (zenon_L384_); trivial. % 8.61/8.79 (* end of lemma zenon_L545_ *) % 8.61/8.79 assert (zenon_L546_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H1ae zenon_H2c3. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_H30. zenon_intro zenon_H1af. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_H14e. zenon_intro zenon_H1b0. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb3. zenon_intro zenon_H1b1. % 8.61/8.79 apply (zenon_L544_); trivial. % 8.61/8.79 (* end of lemma zenon_L546_ *) % 8.61/8.79 assert (zenon_L547_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H1f2 zenon_H154. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1f2). zenon_intro zenon_H191. zenon_intro zenon_H1f3. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H93. zenon_intro zenon_H183. % 8.61/8.79 apply (zenon_L97_); trivial. % 8.61/8.79 (* end of lemma zenon_L547_ *) % 8.61/8.79 assert (zenon_L548_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H207 zenon_H2c3. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H207). zenon_intro zenon_H3c. zenon_intro zenon_H208. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H208). zenon_intro zenon_Hbd. zenon_intro zenon_H1b0. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb3. zenon_intro zenon_H1b1. % 8.61/8.79 apply (zenon_L544_); trivial. % 8.61/8.79 (* end of lemma zenon_L548_ *) % 8.61/8.79 assert (zenon_L549_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H215 zenon_H2c3. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H215). zenon_intro zenon_H1b1. zenon_intro zenon_H216. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H216). zenon_intro zenon_Hb3. zenon_intro zenon_H183. % 8.61/8.79 apply (zenon_L544_); trivial. % 8.61/8.79 (* end of lemma zenon_L549_ *) % 8.61/8.79 assert (zenon_L550_ : (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H127 zenon_H6b zenon_Hd6. % 8.61/8.79 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e0) (e3)))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_H127. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H6b. % 8.61/8.79 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 8.61/8.79 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 8.61/8.79 congruence. % 8.61/8.79 apply zenon_H21. apply refl_equal. % 8.61/8.79 apply zenon_H279. apply sym_equal. exact zenon_Hd6. % 8.61/8.79 (* end of lemma zenon_L550_ *) % 8.61/8.79 assert (zenon_L551_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H105 zenon_Hd1 zenon_H6b zenon_H127 zenon_Hff zenon_H3c zenon_Hd0 zenon_Hb3. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H30 | zenon_intro zenon_H106 ]. % 8.61/8.79 apply (zenon_L47_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H107 ]. % 8.61/8.79 apply (zenon_L550_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfe | zenon_intro zenon_H103 ]. % 8.61/8.79 apply (zenon_L59_); trivial. % 8.61/8.79 apply (zenon_L60_); trivial. % 8.61/8.79 (* end of lemma zenon_L551_ *) % 8.61/8.79 assert (zenon_L552_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H11f zenon_H24 zenon_H153 zenon_H78 zenon_H105 zenon_He4 zenon_H6b zenon_H127 zenon_Hff zenon_H3c zenon_Hd0 zenon_Hb3. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.61/8.79 apply (zenon_L303_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.61/8.79 apply (zenon_L551_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.61/8.79 apply (zenon_L65_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H30 | zenon_intro zenon_H106 ]. % 8.61/8.79 apply (zenon_L66_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H107 ]. % 8.61/8.79 apply (zenon_L550_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfe | zenon_intro zenon_H103 ]. % 8.61/8.79 apply (zenon_L59_); trivial. % 8.61/8.79 apply (zenon_L60_); trivial. % 8.61/8.79 (* end of lemma zenon_L552_ *) % 8.61/8.79 assert (zenon_L553_ : (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> False). % 8.61/8.79 do 0 intro. intros zenon_Ha3 zenon_H1b1 zenon_Hf4. % 8.61/8.79 cut (((op (e3) (e1)) = (e3)) = ((e1) = (e3))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_Ha3. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H1b1. % 8.61/8.79 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.61/8.79 cut (((op (e3) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H29e]. % 8.61/8.79 congruence. % 8.61/8.79 exact (zenon_H29e zenon_Hf4). % 8.61/8.79 apply zenon_H58. apply refl_equal. % 8.61/8.79 (* end of lemma zenon_L553_ *) % 8.61/8.79 assert (zenon_L554_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (op (e2) (e1))) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H336 zenon_Hb3 zenon_Hd0 zenon_H3c zenon_Hff zenon_H127 zenon_He4 zenon_H105 zenon_H78 zenon_H153 zenon_H24 zenon_H11f zenon_H74 zenon_H73 zenon_H56 zenon_Ha3 zenon_H1b1. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.61/8.79 apply (zenon_L552_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.61/8.79 apply (zenon_L20_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.61/8.79 apply (zenon_L99_); trivial. % 8.61/8.79 apply (zenon_L553_); trivial. % 8.61/8.79 (* end of lemma zenon_L554_ *) % 8.61/8.79 assert (zenon_L555_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H2e8 zenon_Hc2 zenon_H24 zenon_Ha8 zenon_H93 zenon_H3c zenon_H4c zenon_H1d9 zenon_H1b1. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2e8); [ zenon_intro zenon_H276 | zenon_intro zenon_H2e9 ]. % 8.61/8.79 apply (zenon_L341_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2e9); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H2ea ]. % 8.61/8.79 apply (zenon_L32_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_H99 | zenon_intro zenon_H98 ]. % 8.61/8.79 apply (zenon_L342_); trivial. % 8.61/8.79 apply (zenon_L375_); trivial. % 8.61/8.79 (* end of lemma zenon_L555_ *) % 8.61/8.79 assert (zenon_L556_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H2a2 zenon_H25 zenon_H24 zenon_H73 zenon_H67 zenon_H169 zenon_H1b1 zenon_H197 zenon_H3c zenon_H6b zenon_H164 zenon_H192 zenon_H19a zenon_H62. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.61/8.79 apply (zenon_L2_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.61/8.79 apply (zenon_L499_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.61/8.79 apply (zenon_L535_); trivial. % 8.61/8.79 apply (zenon_L416_); trivial. % 8.61/8.79 (* end of lemma zenon_L556_ *) % 8.61/8.79 assert (zenon_L557_ : ((op (e3) (e1)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H1b1 zenon_H274 zenon_H1dd. % 8.61/8.79 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H2cb | zenon_intro zenon_H2cc ]. % 8.61/8.79 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e0) (e1)) = (op (e3) (e1)))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_H1dd. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H2cb. % 8.61/8.79 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2cc]. % 8.61/8.79 cut (((op (e3) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2cd]. % 8.61/8.79 congruence. % 8.61/8.79 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e0) (e1)))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_H2cd. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H1b1. % 8.61/8.79 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2d1]. % 8.61/8.79 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2cc]. % 8.61/8.79 congruence. % 8.61/8.79 apply zenon_H2cc. apply refl_equal. % 8.61/8.79 apply zenon_H2d1. apply sym_equal. exact zenon_H274. % 8.61/8.79 apply zenon_H2cc. apply refl_equal. % 8.61/8.79 apply zenon_H2cc. apply refl_equal. % 8.61/8.79 (* end of lemma zenon_L557_ *) % 8.61/8.79 assert (zenon_L558_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H73 zenon_H87 zenon_Ha3. % 8.61/8.79 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H58 ]. % 8.61/8.79 cut (((e3) = (e3)) = ((e1) = (e3))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_Ha3. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_Ha4. % 8.61/8.79 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.61/8.79 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 8.61/8.79 congruence. % 8.61/8.79 cut (((op (e1) (e0)) = (e1)) = ((e3) = (e1))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_Ha5. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H73. % 8.61/8.79 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.61/8.79 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H30e]. % 8.61/8.79 congruence. % 8.61/8.79 exact (zenon_H30e zenon_H87). % 8.61/8.79 apply zenon_H40. apply refl_equal. % 8.61/8.79 apply zenon_H58. apply refl_equal. % 8.61/8.79 apply zenon_H58. apply refl_equal. % 8.61/8.79 (* end of lemma zenon_L558_ *) % 8.61/8.79 assert (zenon_L559_ : ((op (e3) (e1)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H1b1 zenon_Ha2 zenon_Hf3. % 8.61/8.79 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H2cb | zenon_intro zenon_H2cc ]. % 8.61/8.79 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e1) (e1)) = (op (e3) (e1)))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_Hf3. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H2cb. % 8.61/8.79 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2cc]. % 8.61/8.79 cut (((op (e3) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H354]. % 8.61/8.79 congruence. % 8.61/8.79 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e1) (e1)))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_H354. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H1b1. % 8.61/8.79 cut (((e3) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H355]. % 8.61/8.79 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2cc]. % 8.61/8.79 congruence. % 8.61/8.79 apply zenon_H2cc. apply refl_equal. % 8.61/8.79 apply zenon_H355. apply sym_equal. exact zenon_Ha2. % 8.61/8.79 apply zenon_H2cc. apply refl_equal. % 8.61/8.79 apply zenon_H2cc. apply refl_equal. % 8.61/8.79 (* end of lemma zenon_L559_ *) % 8.61/8.79 assert (zenon_L560_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H134 zenon_H276 zenon_Ha7. % 8.61/8.79 cut (((op (e0) (e2)) = (e3)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_H134. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H276. % 8.61/8.79 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2f7]. % 8.61/8.79 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 8.61/8.79 congruence. % 8.61/8.79 apply zenon_H27. apply refl_equal. % 8.61/8.79 apply zenon_H2f7. apply sym_equal. exact zenon_Ha7. % 8.61/8.79 (* end of lemma zenon_L560_ *) % 8.61/8.79 assert (zenon_L561_ : (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e1)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H7d zenon_H3c zenon_H16b. % 8.61/8.79 cut (((op (e2) (e3)) = (e2)) = ((e1) = (e2))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_H7d. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H3c. % 8.61/8.79 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.61/8.79 cut (((op (e2) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H356]. % 8.61/8.79 congruence. % 8.61/8.79 exact (zenon_H356 zenon_H16b). % 8.61/8.79 apply zenon_H4b. apply refl_equal. % 8.61/8.79 (* end of lemma zenon_L561_ *) % 8.61/8.79 assert (zenon_L562_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H19a zenon_H143 zenon_H192 zenon_Hb3 zenon_H109 zenon_He7 zenon_He8 zenon_H197 zenon_Hff zenon_H30 zenon_H2d8 zenon_H3b zenon_H1f6 zenon_H1b1 zenon_H169. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H165 | zenon_intro zenon_H19b ]. % 8.61/8.79 apply (zenon_L249_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H15a | zenon_intro zenon_H19c ]. % 8.61/8.79 apply (zenon_L474_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H191 | zenon_intro zenon_H196 ]. % 8.61/8.79 apply (zenon_L198_); trivial. % 8.61/8.79 apply (zenon_L432_); trivial. % 8.61/8.79 (* end of lemma zenon_L562_ *) % 8.61/8.79 assert (zenon_L563_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H329 zenon_H78 zenon_Ha8 zenon_H16b zenon_H7d zenon_H19a zenon_H143 zenon_H192 zenon_Hb3 zenon_H109 zenon_He7 zenon_H197 zenon_Hff zenon_H30 zenon_H2d8 zenon_H3b zenon_H1f6 zenon_H1b1 zenon_H169. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hfe | zenon_intro zenon_H32a ]. % 8.61/8.79 apply (zenon_L394_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H108 | zenon_intro zenon_H32b ]. % 8.61/8.79 apply (zenon_L471_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H3c | zenon_intro zenon_He8 ]. % 8.61/8.79 apply (zenon_L561_); trivial. % 8.61/8.79 apply (zenon_L562_); trivial. % 8.61/8.79 (* end of lemma zenon_L563_ *) % 8.61/8.79 assert (zenon_L564_ : (((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 (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H2d4 zenon_H14e zenon_H170 zenon_H71 zenon_H29f zenon_H3b zenon_H9a zenon_Ha7 zenon_H2d2. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H2d5 ]. % 8.61/8.79 apply (zenon_L111_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H2d6 ]. % 8.61/8.79 apply (zenon_L266_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_Hbd | zenon_intro zenon_H98 ]. % 8.61/8.79 apply (zenon_L513_); trivial. % 8.61/8.79 apply (zenon_L358_); trivial. % 8.61/8.79 (* end of lemma zenon_L564_ *) % 8.61/8.79 assert (zenon_L565_ : ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H3b zenon_H7e zenon_H90. % 8.61/8.79 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H3e ]. % 8.61/8.79 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e0) (e2)) = (op (e2) (e2)))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_H90. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H95. % 8.61/8.79 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 8.61/8.79 cut (((op (e2) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H357]. % 8.61/8.79 congruence. % 8.61/8.79 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e0) (e2)))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_H357. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H3b. % 8.61/8.79 cut (((e2) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2fe]. % 8.61/8.79 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 8.61/8.79 congruence. % 8.61/8.79 apply zenon_H3e. apply refl_equal. % 8.61/8.79 apply zenon_H2fe. apply sym_equal. exact zenon_H7e. % 8.61/8.79 apply zenon_H3e. apply refl_equal. % 8.61/8.79 apply zenon_H3e. apply refl_equal. % 8.61/8.79 (* end of lemma zenon_L565_ *) % 8.61/8.79 assert (zenon_L566_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((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) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((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). % 8.61/8.79 do 0 intro. intros zenon_H2df zenon_H2d2 zenon_H9a zenon_H170 zenon_H14e zenon_H2d4 zenon_Hab zenon_H73 zenon_H7d zenon_H300 zenon_H30 zenon_H153 zenon_H29f zenon_H90 zenon_H3b zenon_H134 zenon_Ha7. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.61/8.79 apply (zenon_L564_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.61/8.79 apply (zenon_L93_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.61/8.79 apply (zenon_L396_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H24 | zenon_intro zenon_H301 ]. % 8.61/8.79 apply (zenon_L303_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H71 | zenon_intro zenon_H302 ]. % 8.61/8.79 apply (zenon_L266_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H7e | zenon_intro zenon_H276 ]. % 8.61/8.79 apply (zenon_L565_); trivial. % 8.61/8.79 apply (zenon_L560_); trivial. % 8.61/8.79 (* end of lemma zenon_L566_ *) % 8.61/8.79 assert (zenon_L567_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 8.61/8.79 do 0 intro. intros zenon_Hba zenon_Ha3 zenon_H73 zenon_Hf3 zenon_H1b1 zenon_H276 zenon_H134 zenon_H108 zenon_Ha8. % 8.61/8.79 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.61/8.79 apply (zenon_L558_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.61/8.79 apply (zenon_L559_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.61/8.79 apply (zenon_L560_); trivial. % 8.61/8.79 apply (zenon_L471_); trivial. % 8.61/8.79 (* end of lemma zenon_L567_ *) % 8.61/8.79 assert (zenon_L568_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H300 zenon_Had zenon_Hf6 zenon_H29f zenon_H90 zenon_H3b zenon_Hba zenon_Ha3 zenon_H73 zenon_Hf3 zenon_H1b1 zenon_H134 zenon_H108 zenon_Ha8. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H24 | zenon_intro zenon_H301 ]. % 8.61/8.79 apply (zenon_L397_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H71 | zenon_intro zenon_H302 ]. % 8.61/8.79 apply (zenon_L266_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H7e | zenon_intro zenon_H276 ]. % 8.61/8.79 apply (zenon_L565_); trivial. % 8.61/8.79 apply (zenon_L567_); trivial. % 8.61/8.79 (* end of lemma zenon_L568_ *) % 8.61/8.79 assert (zenon_L569_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (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 (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H2df zenon_H25 zenon_H66 zenon_H67 zenon_H7d zenon_H329 zenon_H78 zenon_Ha8 zenon_H134 zenon_H1b1 zenon_Hf3 zenon_H73 zenon_Ha3 zenon_Hba zenon_H90 zenon_H29f zenon_Had zenon_H300 zenon_H3b zenon_H3a zenon_H2d8 zenon_H30 zenon_Hff zenon_H15a zenon_H197 zenon_He7 zenon_H109 zenon_Hb3. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.61/8.79 apply (zenon_L19_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.61/8.79 apply (zenon_L110_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.61/8.79 apply (zenon_L396_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hfe | zenon_intro zenon_H32a ]. % 8.61/8.79 apply (zenon_L394_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H108 | zenon_intro zenon_H32b ]. % 8.61/8.79 apply (zenon_L568_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H3c | zenon_intro zenon_He8 ]. % 8.61/8.79 apply (zenon_L6_); trivial. % 8.61/8.79 apply (zenon_L474_); trivial. % 8.61/8.79 (* end of lemma zenon_L569_ *) % 8.61/8.79 assert (zenon_L570_ : (((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 (e3) (e1)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H2d4 zenon_H14e zenon_H170 zenon_Hf4 zenon_H3b zenon_H9a zenon_H1d9 zenon_H1b1. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H2d5 ]. % 8.61/8.79 apply (zenon_L111_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H2d6 ]. % 8.61/8.79 apply (zenon_L319_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_Hbd | zenon_intro zenon_H98 ]. % 8.61/8.79 apply (zenon_L513_); trivial. % 8.61/8.79 apply (zenon_L375_); trivial. % 8.61/8.79 (* end of lemma zenon_L570_ *) % 8.61/8.79 assert (zenon_L571_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (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))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H2e8 zenon_Ha3 zenon_H2d2 zenon_H9a zenon_H29f zenon_H71 zenon_H170 zenon_H14e zenon_H2d4 zenon_Ha8 zenon_H3b zenon_H1d9 zenon_H1b1. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2e8); [ zenon_intro zenon_H276 | zenon_intro zenon_H2e9 ]. % 8.61/8.79 apply (zenon_L245_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2e9); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H2ea ]. % 8.61/8.79 apply (zenon_L564_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_H99 | zenon_intro zenon_H98 ]. % 8.61/8.79 apply (zenon_L346_); trivial. % 8.61/8.79 apply (zenon_L375_); trivial. % 8.61/8.79 (* end of lemma zenon_L571_ *) % 8.61/8.79 assert (zenon_L572_ : (~((op (e1) (op (e1) (e1))) = (e1))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H41 zenon_H73 zenon_H358. % 8.61/8.79 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (op (e1) (e1))) = (e1))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_H41. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H73. % 8.61/8.79 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.61/8.79 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H359]. % 8.61/8.79 congruence. % 8.61/8.79 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_H43 | zenon_intro zenon_H44 ]. % 8.61/8.79 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e0)) = (op (e1) (op (e1) (e1))))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_H359. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H43. % 8.61/8.79 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 8.61/8.79 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H35a]. % 8.61/8.79 congruence. % 8.61/8.79 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H35b]. % 8.61/8.79 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.61/8.79 congruence. % 8.61/8.79 apply zenon_H40. apply refl_equal. % 8.61/8.79 exact (zenon_H35b zenon_H358). % 8.61/8.79 apply zenon_H44. apply refl_equal. % 8.61/8.79 apply zenon_H44. apply refl_equal. % 8.61/8.79 apply zenon_H40. apply refl_equal. % 8.61/8.79 (* end of lemma zenon_L572_ *) % 8.61/8.79 assert (zenon_L573_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H1d9 zenon_H1df zenon_Hc3. % 8.61/8.79 cut (((op (e3) (e1)) = (e0)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_H1d9. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H1df. % 8.61/8.79 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H171]. % 8.61/8.79 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2cc]. % 8.61/8.79 congruence. % 8.61/8.79 apply zenon_H2cc. apply refl_equal. % 8.61/8.79 apply zenon_H171. apply sym_equal. exact zenon_Hc3. % 8.61/8.79 (* end of lemma zenon_L573_ *) % 8.61/8.79 assert (zenon_L574_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (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) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H2d4 zenon_H1df zenon_Ha8 zenon_H108 zenon_H134 zenon_Hf3 zenon_H73 zenon_Ha3 zenon_Hba zenon_H90 zenon_H29f zenon_Had zenon_H300 zenon_H3b zenon_H9a zenon_H1d9 zenon_H1b1. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H2d5 ]. % 8.61/8.79 apply (zenon_L573_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H2d6 ]. % 8.61/8.79 apply (zenon_L568_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_Hbd | zenon_intro zenon_H98 ]. % 8.61/8.79 apply (zenon_L513_); trivial. % 8.61/8.79 apply (zenon_L375_); trivial. % 8.61/8.79 (* end of lemma zenon_L574_ *) % 8.61/8.79 assert (zenon_L575_ : (((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)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H2b5 zenon_Hd0 zenon_Hb4 zenon_H1d9 zenon_H9a zenon_H300 zenon_Had zenon_H29f zenon_H90 zenon_Hba zenon_Ha3 zenon_H73 zenon_Hf3 zenon_H134 zenon_Ha8 zenon_H1df zenon_H2d4 zenon_H19a zenon_H143 zenon_H192 zenon_H109 zenon_He7 zenon_He8 zenon_H197 zenon_Hff zenon_H30 zenon_H2d8 zenon_H3b zenon_H1f6 zenon_H1b1 zenon_H169. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H2b6 ]. % 8.61/8.79 apply (zenon_L47_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H35 | zenon_intro zenon_H2b7 ]. % 8.61/8.79 apply (zenon_L119_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H108 | zenon_intro zenon_Hb3 ]. % 8.61/8.79 apply (zenon_L574_); trivial. % 8.61/8.79 apply (zenon_L562_); trivial. % 8.61/8.79 (* end of lemma zenon_L575_ *) % 8.61/8.79 assert (zenon_L576_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (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 (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H329 zenon_H78 zenon_H3a zenon_H2b5 zenon_Hd0 zenon_Hb4 zenon_H1d9 zenon_H9a zenon_H300 zenon_Had zenon_H29f zenon_H90 zenon_Hba zenon_Ha3 zenon_H73 zenon_Hf3 zenon_H134 zenon_Ha8 zenon_H1df zenon_H2d4 zenon_H19a zenon_H143 zenon_H192 zenon_H109 zenon_He7 zenon_H197 zenon_Hff zenon_H30 zenon_H2d8 zenon_H3b zenon_H1f6 zenon_H1b1 zenon_H169. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hfe | zenon_intro zenon_H32a ]. % 8.61/8.79 apply (zenon_L394_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H108 | zenon_intro zenon_H32b ]. % 8.61/8.79 apply (zenon_L574_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H3c | zenon_intro zenon_He8 ]. % 8.61/8.79 apply (zenon_L6_); trivial. % 8.61/8.79 apply (zenon_L575_); trivial. % 8.61/8.79 (* end of lemma zenon_L576_ *) % 8.61/8.79 assert (zenon_L577_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H1a0 zenon_H1f6 zenon_H3b. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1a0). zenon_intro zenon_H24. zenon_intro zenon_H1a1. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1a1). zenon_intro zenon_H143. zenon_intro zenon_H1a2. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1a2). zenon_intro zenon_H93. zenon_intro zenon_H191. % 8.61/8.79 apply (zenon_L198_); trivial. % 8.61/8.79 (* end of lemma zenon_L577_ *) % 8.61/8.79 assert (zenon_L578_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H1a3 zenon_H153 zenon_H30. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1a3). zenon_intro zenon_H24. zenon_intro zenon_H1a4. % 8.61/8.79 apply (zenon_L303_); trivial. % 8.61/8.79 (* end of lemma zenon_L578_ *) % 8.61/8.79 assert (zenon_L579_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H1b7 zenon_H30 zenon_H31. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_H73. zenon_intro zenon_H1b8. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1b8). zenon_intro zenon_H6b. zenon_intro zenon_H177. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H177). zenon_intro zenon_H1e. zenon_intro zenon_H1e. % 8.61/8.79 apply (zenon_L4_); trivial. % 8.61/8.79 (* end of lemma zenon_L579_ *) % 8.61/8.79 assert (zenon_L580_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H1bb zenon_H153 zenon_H30. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1bb). zenon_intro zenon_H73. zenon_intro zenon_H1bc. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1bc). zenon_intro zenon_H6b. zenon_intro zenon_H17d. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H17d). zenon_intro zenon_H143. zenon_intro zenon_H24. % 8.61/8.79 apply (zenon_L303_); trivial. % 8.61/8.79 (* end of lemma zenon_L580_ *) % 8.61/8.79 assert (zenon_L581_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H1c8 zenon_H22d zenon_H1d9 zenon_H1d7 zenon_Ha8 zenon_H173 zenon_H192 zenon_Ha3 zenon_H2b8 zenon_H67 zenon_H197 zenon_H2b zenon_Hab zenon_Hc2 zenon_H1f6 zenon_H7d zenon_H78 zenon_H127 zenon_H31 zenon_H25 zenon_H22e zenon_H153 zenon_H170 zenon_Hc5 zenon_H3a zenon_H2a2 zenon_H29f zenon_H2d2 zenon_H2d4 zenon_H145 zenon_H10c zenon_Hb4 zenon_H32e zenon_H109 zenon_He7 zenon_Hff zenon_H2d8 zenon_H329 zenon_H2a5 zenon_H129 zenon_H12b zenon_H2fc zenon_H1b1. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_H29. zenon_intro zenon_H1c9. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1c9). zenon_intro zenon_H15a. zenon_intro zenon_H19f. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H19f). zenon_intro zenon_H7e. zenon_intro zenon_Hc8. % 8.61/8.79 apply (zenon_L483_); trivial. % 8.61/8.79 (* end of lemma zenon_L581_ *) % 8.61/8.79 assert (zenon_L582_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H2b8 zenon_H67 zenon_H30 zenon_Hb4 zenon_H73 zenon_H15a zenon_H197 zenon_H59 zenon_H1b1. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H2b9 ]. % 8.61/8.79 apply (zenon_L343_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_H35 | zenon_intro zenon_H2ba ]. % 8.61/8.79 apply (zenon_L119_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H16b | zenon_intro zenon_He5 ]. % 8.61/8.79 apply (zenon_L472_); trivial. % 8.61/8.79 apply (zenon_L479_); trivial. % 8.61/8.79 (* end of lemma zenon_L582_ *) % 8.61/8.79 assert (zenon_L583_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H1f2 zenon_H1f6 zenon_H3b. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1f2). zenon_intro zenon_H191. zenon_intro zenon_H1f3. % 8.61/8.79 apply (zenon_L198_); trivial. % 8.61/8.79 (* end of lemma zenon_L583_ *) % 8.61/8.79 assert (zenon_L584_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H35 zenon_H108 zenon_H7d. % 8.61/8.79 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H79 | zenon_intro zenon_H4b ]. % 8.61/8.79 cut (((e2) = (e2)) = ((e1) = (e2))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_H7d. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H79. % 8.61/8.79 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.61/8.79 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hce]. % 8.61/8.79 congruence. % 8.61/8.79 cut (((op (e1) (e3)) = (e1)) = ((e2) = (e1))). % 8.61/8.79 intro zenon_D_pnotp. % 8.61/8.79 apply zenon_Hce. % 8.61/8.79 rewrite <- zenon_D_pnotp. % 8.61/8.79 exact zenon_H35. % 8.61/8.79 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.61/8.79 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H35c]. % 8.61/8.79 congruence. % 8.61/8.79 exact (zenon_H35c zenon_H108). % 8.61/8.79 apply zenon_H40. apply refl_equal. % 8.61/8.79 apply zenon_H4b. apply refl_equal. % 8.61/8.79 apply zenon_H4b. apply refl_equal. % 8.61/8.79 (* end of lemma zenon_L584_ *) % 8.61/8.79 assert (zenon_L585_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H2b8 zenon_H67 zenon_H30 zenon_H7d zenon_H108 zenon_H15a zenon_H197 zenon_H59 zenon_H1b1. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H2b9 ]. % 8.61/8.79 apply (zenon_L343_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_H35 | zenon_intro zenon_H2ba ]. % 8.61/8.79 apply (zenon_L584_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H16b | zenon_intro zenon_He5 ]. % 8.61/8.79 apply (zenon_L472_); trivial. % 8.61/8.79 apply (zenon_L479_); trivial. % 8.61/8.79 (* end of lemma zenon_L585_ *) % 8.61/8.79 assert (zenon_L586_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> ((op (e1) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H19a zenon_H143 zenon_H192 zenon_H1b1 zenon_H59 zenon_H108 zenon_H7d zenon_H30 zenon_H67 zenon_H2b8 zenon_H1f6 zenon_H201 zenon_H195 zenon_H197. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H165 | zenon_intro zenon_H19b ]. % 8.61/8.79 apply (zenon_L249_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H15a | zenon_intro zenon_H19c ]. % 8.61/8.79 apply (zenon_L585_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H191 | zenon_intro zenon_H196 ]. % 8.61/8.79 apply (zenon_L217_); trivial. % 8.61/8.79 apply (zenon_L126_); trivial. % 8.61/8.79 (* end of lemma zenon_L586_ *) % 8.61/8.79 assert (zenon_L587_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (((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) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H331 zenon_Hc2 zenon_H169 zenon_H3b zenon_H2d8 zenon_Hff zenon_He7 zenon_H109 zenon_H16b zenon_Ha8 zenon_H78 zenon_H329 zenon_H197 zenon_H201 zenon_H1f6 zenon_H2b8 zenon_H67 zenon_H30 zenon_H7d zenon_H108 zenon_H1b1 zenon_H192 zenon_H143 zenon_H19a zenon_H59. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H331); [ zenon_intro zenon_H103 | zenon_intro zenon_H332 ]. % 8.61/8.79 apply (zenon_L201_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H332); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H333 ]. % 8.61/8.79 apply (zenon_L563_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H333); [ zenon_intro zenon_H195 | zenon_intro zenon_H5a ]. % 8.61/8.79 apply (zenon_L586_); trivial. % 8.61/8.79 apply (zenon_L15_); trivial. % 8.61/8.79 (* end of lemma zenon_L587_ *) % 8.61/8.79 assert (zenon_L588_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (((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) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H303 zenon_H331 zenon_Hc2 zenon_H169 zenon_H3b zenon_H2d8 zenon_Hff zenon_He7 zenon_H109 zenon_Ha8 zenon_H78 zenon_H329 zenon_H197 zenon_H201 zenon_H1f6 zenon_H2b8 zenon_H67 zenon_H30 zenon_H7d zenon_H108 zenon_H1b1 zenon_H192 zenon_H143 zenon_H19a zenon_H59. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.61/8.79 apply (zenon_L261_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.61/8.79 apply (zenon_L585_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.61/8.79 apply (zenon_L396_); trivial. % 8.61/8.79 apply (zenon_L587_); trivial. % 8.61/8.79 (* end of lemma zenon_L588_ *) % 8.61/8.79 assert (zenon_L589_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H2b5 zenon_Hd0 zenon_H16b zenon_H195 zenon_H201 zenon_H2b8 zenon_H67 zenon_H7d zenon_H59 zenon_H19a zenon_H143 zenon_H192 zenon_H109 zenon_He7 zenon_He8 zenon_H197 zenon_Hff zenon_H30 zenon_H2d8 zenon_H3b zenon_H1f6 zenon_H1b1 zenon_H169. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H2b6 ]. % 8.61/8.79 apply (zenon_L47_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H35 | zenon_intro zenon_H2b7 ]. % 8.61/8.79 apply (zenon_L106_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H108 | zenon_intro zenon_Hb3 ]. % 8.61/8.79 apply (zenon_L586_); trivial. % 8.61/8.79 apply (zenon_L562_); trivial. % 8.61/8.79 (* end of lemma zenon_L589_ *) % 8.61/8.79 assert (zenon_L590_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H329 zenon_H78 zenon_H303 zenon_H3a zenon_H331 zenon_Hc2 zenon_H169 zenon_H1b1 zenon_H1f6 zenon_H3b zenon_H2d8 zenon_H30 zenon_Hff zenon_H197 zenon_He7 zenon_H109 zenon_H192 zenon_H143 zenon_H19a zenon_H59 zenon_H7d zenon_H67 zenon_H2b8 zenon_H201 zenon_H16b zenon_Hd0 zenon_H2b5 zenon_Ha8. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hfe | zenon_intro zenon_H32a ]. % 8.61/8.79 apply (zenon_L394_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H108 | zenon_intro zenon_H32b ]. % 8.61/8.79 apply (zenon_L588_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H3c | zenon_intro zenon_He8 ]. % 8.61/8.79 apply (zenon_L6_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H331); [ zenon_intro zenon_H103 | zenon_intro zenon_H332 ]. % 8.61/8.79 apply (zenon_L201_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H332); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H333 ]. % 8.61/8.79 apply (zenon_L562_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H333); [ zenon_intro zenon_H195 | zenon_intro zenon_H5a ]. % 8.61/8.79 apply (zenon_L589_); trivial. % 8.61/8.79 apply (zenon_L439_); trivial. % 8.61/8.79 (* end of lemma zenon_L590_ *) % 8.61/8.79 assert (zenon_L591_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> False). % 8.61/8.79 do 0 intro. intros zenon_H2a2 zenon_H31 zenon_H73 zenon_H169 zenon_H1b1 zenon_H1f6 zenon_H3b zenon_H2d8 zenon_H30 zenon_Hff zenon_H197 zenon_He7 zenon_H109 zenon_Hb3 zenon_H192 zenon_H19a zenon_H7d zenon_Ha8 zenon_H78 zenon_H329 zenon_H2b8 zenon_H67 zenon_Ha3 zenon_H59 zenon_H303 zenon_H62. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.61/8.79 apply (zenon_L4_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.61/8.79 apply (zenon_L499_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.61/8.79 apply (zenon_L261_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.61/8.79 apply (zenon_L481_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.61/8.79 apply (zenon_L396_); trivial. % 8.61/8.79 apply (zenon_L563_); trivial. % 8.61/8.79 apply (zenon_L416_); trivial. % 8.61/8.79 (* end of lemma zenon_L591_ *) % 8.61/8.79 assert (zenon_L592_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H21f zenon_H1f6 zenon_H3b. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H21f). zenon_intro zenon_H98. zenon_intro zenon_H220. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H220). zenon_intro zenon_H195. zenon_intro zenon_H1a2. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1a2). zenon_intro zenon_H93. zenon_intro zenon_H191. % 8.61/8.79 apply (zenon_L198_); trivial. % 8.61/8.79 (* end of lemma zenon_L592_ *) % 8.61/8.79 assert (zenon_L593_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((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))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (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)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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 (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.61/8.79 do 0 intro. intros zenon_H2f8 zenon_H34d zenon_H105 zenon_He4 zenon_H2bf zenon_H2e2 zenon_Hf8 zenon_H2a3 zenon_H36 zenon_H124 zenon_H11f zenon_Hf9 zenon_H285 zenon_H27f zenon_H282 zenon_H150 zenon_Hb7 zenon_H2c9 zenon_H295 zenon_H1dc zenon_H2c0 zenon_H270 zenon_H1f zenon_H16d zenon_H2f3 zenon_H164 zenon_H2fc zenon_H3a zenon_H73 zenon_Hb4 zenon_H2e8 zenon_H2a4 zenon_H1dd zenon_H336 zenon_H2a1 zenon_H137 zenon_H2df zenon_H9a zenon_H300 zenon_H90 zenon_H134 zenon_Hf3 zenon_Hba zenon_H35d zenon_H35e zenon_H6c zenon_H12b zenon_H129 zenon_H2a5 zenon_H32e zenon_H10c zenon_H145 zenon_H2d4 zenon_H2d2 zenon_H29f zenon_Hc5 zenon_H170 zenon_H153 zenon_H22e zenon_H25 zenon_Hab zenon_H2b zenon_H22d zenon_H127 zenon_H173 zenon_H331 zenon_Hd0 zenon_H2b5 zenon_H1d3 zenon_Hc2 zenon_H303 zenon_H329 zenon_H78 zenon_H7d zenon_H19a zenon_H192 zenon_H109 zenon_He7 zenon_Hff zenon_H2d8 zenon_H169 zenon_H31 zenon_H2a2 zenon_H74 zenon_H197 zenon_H67 zenon_H2b8 zenon_Ha3 zenon_H1f6 zenon_Ha8 zenon_H1d7 zenon_H1d9 zenon_H1b1. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c1 ]. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.61/8.79 apply (zenon_L303_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.61/8.79 apply (zenon_L119_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H118. zenon_intro zenon_H18a. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.61/8.79 apply (zenon_L308_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.61/8.79 apply (zenon_L309_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.61/8.79 apply (zenon_L116_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.61/8.79 apply (zenon_L118_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.61/8.79 apply (zenon_L514_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.61/8.79 apply (zenon_L515_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.61/8.79 apply (zenon_L516_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.61/8.79 apply (zenon_L310_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.61/8.79 apply (zenon_L129_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.61/8.79 apply (zenon_L518_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.61/8.79 apply (zenon_L163_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1a6). zenon_intro zenon_H24. zenon_intro zenon_H1a7. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H143. zenon_intro zenon_H1a8. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hbd. zenon_intro zenon_H3c. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H331); [ zenon_intro zenon_H103 | zenon_intro zenon_H332 ]. % 8.61/8.79 apply (zenon_L123_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H332); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H333 ]. % 8.61/8.79 apply (zenon_L533_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H333); [ zenon_intro zenon_H195 | zenon_intro zenon_H5a ]. % 8.61/8.79 apply (zenon_L368_); trivial. % 8.61/8.79 apply (zenon_L384_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.61/8.79 apply (zenon_L135_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_H30. zenon_intro zenon_H1af. % 8.61/8.79 apply (zenon_L303_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.61/8.79 apply (zenon_L443_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.61/8.79 apply (zenon_L444_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.61/8.79 apply (zenon_L311_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.61/8.79 apply (zenon_L520_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.61/8.79 apply (zenon_L536_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.61/8.79 apply (zenon_L445_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.61/8.79 apply (zenon_L522_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.61/8.79 apply (zenon_L523_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.61/8.79 apply (zenon_L146_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.61/8.79 apply (zenon_L524_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.61/8.79 apply (zenon_L148_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.61/8.79 apply (zenon_L151_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.61/8.79 apply (zenon_L179_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.61/8.79 apply (zenon_L525_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.61/8.79 apply (zenon_L355_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.61/8.79 apply (zenon_L356_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.61/8.79 apply (zenon_L446_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.61/8.79 apply (zenon_L447_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.61/8.79 apply (zenon_L448_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.61/8.79 apply (zenon_L449_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.61/8.79 apply (zenon_L188_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.61/8.79 apply (zenon_L361_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.61/8.79 apply (zenon_L528_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.61/8.79 apply (zenon_L529_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.61/8.79 apply (zenon_L364_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.61/8.79 apply (zenon_L530_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.61/8.79 apply (zenon_L241_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.61/8.79 apply (zenon_L242_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.61/8.79 apply (zenon_L531_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.61/8.79 apply (zenon_L272_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.61/8.79 apply (zenon_L273_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H207). zenon_intro zenon_H3c. zenon_intro zenon_H208. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H208). zenon_intro zenon_Hbd. zenon_intro zenon_H1b0. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb3. zenon_intro zenon_H1b1. % 8.61/8.79 apply (zenon_L533_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.61/8.79 apply (zenon_L451_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.61/8.79 apply (zenon_L452_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.61/8.79 apply (zenon_L322_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.61/8.79 apply (zenon_L275_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.61/8.79 apply (zenon_L537_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.61/8.79 apply (zenon_L373_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.61/8.79 apply (zenon_L538_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.61/8.79 apply (zenon_L539_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.61/8.79 apply (zenon_L540_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.61/8.79 apply (zenon_L378_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.61/8.79 apply (zenon_L379_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.61/8.79 apply (zenon_L541_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.61/8.79 apply (zenon_L542_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.61/8.79 apply (zenon_L382_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.61/8.79 apply (zenon_L383_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.61/8.79 apply (zenon_L385_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.61/8.79 apply (zenon_L454_); trivial. % 8.61/8.79 apply (zenon_L455_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H41. zenon_intro zenon_H4a. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H4a). zenon_intro zenon_H154. zenon_intro zenon_H2c3. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.61/8.79 apply (zenon_L308_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.61/8.79 apply (zenon_L309_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.61/8.79 apply (zenon_L115_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.61/8.79 apply (zenon_L442_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.61/8.79 apply (zenon_L514_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.61/8.79 apply (zenon_L515_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.61/8.79 apply (zenon_L277_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.61/8.79 apply (zenon_L389_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.61/8.79 apply (zenon_L160_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.61/8.79 apply (zenon_L278_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.61/8.79 apply (zenon_L163_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1a6). zenon_intro zenon_H24. zenon_intro zenon_H1a7. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H143. zenon_intro zenon_H1a8. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hbd. zenon_intro zenon_H3c. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.61/8.79 apply (zenon_L543_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.61/8.79 apply (zenon_L535_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.61/8.79 apply (zenon_L22_); trivial. % 8.61/8.79 apply (zenon_L545_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.61/8.79 apply (zenon_L135_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.61/8.79 apply (zenon_L546_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.61/8.79 apply (zenon_L443_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.61/8.79 apply (zenon_L444_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.61/8.79 apply (zenon_L311_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.61/8.79 apply (zenon_L312_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.61/8.79 apply (zenon_L536_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.61/8.79 apply (zenon_L445_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.61/8.79 apply (zenon_L522_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.61/8.79 apply (zenon_L523_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.61/8.79 apply (zenon_L146_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.61/8.79 apply (zenon_L524_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.61/8.79 apply (zenon_L178_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.61/8.79 apply (zenon_L151_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.61/8.79 apply (zenon_L179_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.61/8.79 apply (zenon_L525_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.61/8.79 apply (zenon_L355_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.61/8.79 apply (zenon_L356_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.61/8.79 apply (zenon_L446_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.61/8.79 apply (zenon_L447_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.61/8.79 apply (zenon_L448_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.61/8.79 apply (zenon_L187_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.61/8.79 apply (zenon_L188_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.61/8.79 apply (zenon_L450_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.61/8.79 apply (zenon_L547_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.61/8.79 apply (zenon_L192_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.61/8.79 apply (zenon_L364_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.61/8.79 apply (zenon_L279_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.61/8.79 apply (zenon_L241_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.61/8.79 apply (zenon_L242_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.61/8.79 apply (zenon_L531_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.61/8.79 apply (zenon_L272_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.61/8.79 apply (zenon_L407_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.61/8.79 apply (zenon_L548_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.61/8.79 apply (zenon_L369_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.61/8.79 apply (zenon_L452_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.61/8.79 apply (zenon_L322_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.61/8.79 apply (zenon_L281_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.61/8.79 apply (zenon_L537_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.61/8.79 apply (zenon_L373_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.61/8.79 apply (zenon_L549_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.61/8.79 apply (zenon_L539_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.61/8.79 apply (zenon_L540_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.61/8.79 apply (zenon_L378_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.61/8.79 apply (zenon_L453_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.61/8.79 apply (zenon_L541_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.61/8.79 apply (zenon_L542_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.61/8.79 apply (zenon_L382_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.61/8.79 apply (zenon_L383_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.61/8.79 apply (zenon_L386_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.61/8.79 apply (zenon_L454_); trivial. % 8.61/8.79 apply (zenon_L455_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H4c. zenon_intro zenon_H57. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.61/8.79 apply (zenon_L308_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.61/8.79 apply (zenon_L309_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.61/8.79 apply (zenon_L282_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.61/8.79 apply (zenon_L118_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.61/8.79 apply (zenon_L514_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.61/8.79 apply (zenon_L515_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.61/8.79 apply (zenon_L283_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.61/8.79 apply (zenon_L310_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.61/8.79 apply (zenon_L129_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.61/8.79 apply (zenon_L284_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.61/8.79 apply (zenon_L163_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.61/8.79 apply (zenon_L285_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.61/8.79 apply (zenon_L135_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_H30. zenon_intro zenon_H1af. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_H14e. zenon_intro zenon_H1b0. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb3. zenon_intro zenon_H1b1. % 8.61/8.79 apply (zenon_L554_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.61/8.79 apply (zenon_L410_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.61/8.79 apply (zenon_L444_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.61/8.79 apply (zenon_L311_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.61/8.79 apply (zenon_L520_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.61/8.79 apply (zenon_L286_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.61/8.79 apply (zenon_L445_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.61/8.79 apply (zenon_L522_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.61/8.79 apply (zenon_L523_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.61/8.79 apply (zenon_L146_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.61/8.79 apply (zenon_L524_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.61/8.79 apply (zenon_L411_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.61/8.79 apply (zenon_L151_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.61/8.79 apply (zenon_L179_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.61/8.79 apply (zenon_L287_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.61/8.79 apply (zenon_L355_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.61/8.79 apply (zenon_L356_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.61/8.79 apply (zenon_L412_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.61/8.79 apply (zenon_L447_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.61/8.79 apply (zenon_L448_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.61/8.79 apply (zenon_L449_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.61/8.79 apply (zenon_L188_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.61/8.79 apply (zenon_L450_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1f2). zenon_intro zenon_H191. zenon_intro zenon_H1f3. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H93. zenon_intro zenon_H183. % 8.61/8.79 apply (zenon_L555_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.61/8.79 apply (zenon_L529_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.61/8.79 apply (zenon_L364_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.61/8.79 apply (zenon_L458_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.61/8.79 apply (zenon_L241_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.61/8.79 apply (zenon_L242_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.61/8.79 apply (zenon_L531_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.61/8.79 apply (zenon_L272_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.61/8.79 apply (zenon_L457_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H207). zenon_intro zenon_H3c. zenon_intro zenon_H208. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H208). zenon_intro zenon_Hbd. zenon_intro zenon_H1b0. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb3. zenon_intro zenon_H1b1. % 8.61/8.79 apply (zenon_L554_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.61/8.79 apply (zenon_L451_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.61/8.79 apply (zenon_L452_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.61/8.79 apply (zenon_L322_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.61/8.79 apply (zenon_L323_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.61/8.79 apply (zenon_L293_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.61/8.79 apply (zenon_L373_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H215). zenon_intro zenon_H1b1. zenon_intro zenon_H216. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H216). zenon_intro zenon_Hb3. zenon_intro zenon_H183. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H183). zenon_intro zenon_H6b. zenon_intro zenon_H73. % 8.61/8.79 apply (zenon_L552_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.61/8.79 apply (zenon_L539_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.61/8.79 apply (zenon_L414_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.61/8.79 apply (zenon_L378_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.61/8.79 apply (zenon_L415_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.61/8.79 apply (zenon_L541_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.61/8.79 apply (zenon_L542_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.61/8.79 apply (zenon_L382_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.61/8.79 apply (zenon_L383_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.61/8.79 apply (zenon_L385_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.61/8.79 apply (zenon_L454_); trivial. % 8.61/8.79 apply (zenon_L455_); trivial. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H59. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.61/8.79 apply (zenon_L308_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.61/8.79 apply (zenon_L309_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.61/8.79 apply (zenon_L115_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.61/8.79 apply (zenon_L417_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.61/8.79 apply (zenon_L514_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.61/8.79 apply (zenon_L515_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.61/8.79 apply (zenon_L516_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.61/8.79 apply (zenon_L310_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.61/8.79 apply (zenon_L160_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.61/8.79 apply (zenon_L518_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.61/8.79 apply (zenon_L163_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.61/8.79 apply (zenon_L296_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.61/8.79 apply (zenon_L135_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.61/8.79 apply (zenon_L459_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.61/8.79 apply (zenon_L418_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.61/8.79 apply (zenon_L444_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.61/8.79 apply (zenon_L311_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.61/8.79 apply (zenon_L312_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.61/8.79 apply (zenon_L536_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.61/8.79 apply (zenon_L445_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.61/8.79 apply (zenon_L522_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.61/8.79 apply (zenon_L523_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.61/8.79 apply (zenon_L146_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.61/8.79 apply (zenon_L334_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.61/8.79 apply (zenon_L178_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.61/8.79 apply (zenon_L151_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.61/8.79 apply (zenon_L179_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.61/8.79 apply (zenon_L297_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.61/8.79 apply (zenon_L355_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.61/8.79 apply (zenon_L356_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.61/8.79 apply (zenon_L421_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.61/8.79 apply (zenon_L447_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.61/8.79 apply (zenon_L448_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.61/8.79 apply (zenon_L187_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.61/8.79 apply (zenon_L188_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.61/8.79 apply (zenon_L450_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1f2). zenon_intro zenon_H191. zenon_intro zenon_H1f3. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H93. zenon_intro zenon_H183. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H183). zenon_intro zenon_H6b. zenon_intro zenon_H73. % 8.61/8.79 apply (zenon_L556_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.61/8.79 apply (zenon_L192_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.61/8.79 apply (zenon_L364_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.61/8.79 apply (zenon_L335_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.61/8.79 apply (zenon_L241_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.61/8.79 apply (zenon_L242_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.61/8.79 apply (zenon_L531_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.61/8.79 apply (zenon_L299_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.61/8.79 apply (zenon_L300_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.61/8.79 apply (zenon_L423_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.61/8.79 apply (zenon_L369_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.61/8.79 apply (zenon_L452_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.61/8.79 apply (zenon_L322_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.61/8.79 apply (zenon_L323_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.61/8.79 apply (zenon_L537_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.61/8.79 apply (zenon_L373_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H215). zenon_intro zenon_H1b1. zenon_intro zenon_H216. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H216). zenon_intro zenon_Hb3. zenon_intro zenon_H183. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H183). zenon_intro zenon_H6b. zenon_intro zenon_H73. % 8.61/8.79 apply (zenon_L556_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.61/8.79 apply (zenon_L539_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.61/8.79 apply (zenon_L540_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.61/8.79 apply (zenon_L378_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.61/8.79 apply (zenon_L453_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.61/8.79 apply (zenon_L541_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.61/8.79 apply (zenon_L542_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.61/8.79 apply (zenon_L382_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.61/8.79 apply (zenon_L383_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.61/8.79 apply (zenon_L386_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.61/8.79 apply (zenon_L454_); trivial. % 8.61/8.79 apply (zenon_L455_); trivial. % 8.61/8.79 apply (zenon_L384_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H29 | zenon_intro zenon_H2c2 ]. % 8.61/8.79 apply (zenon_L93_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2c2); [ zenon_intro zenon_H3b | zenon_intro zenon_H98 ]. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 8.61/8.79 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H118. zenon_intro zenon_H18a. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.61/8.79 apply (zenon_L4_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.61/8.79 apply (zenon_L499_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2a4); [ zenon_intro zenon_H26f | zenon_intro zenon_H2ad ]. % 8.61/8.79 apply (zenon_L461_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H274 | zenon_intro zenon_H2ae ]. % 8.61/8.79 apply (zenon_L557_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H276 | zenon_intro zenon_H103 ]. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.61/8.79 apply (zenon_L527_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.61/8.79 apply (zenon_L20_); trivial. % 8.61/8.79 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.61/8.79 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.61/8.80 apply (zenon_L558_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.61/8.80 apply (zenon_L559_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.61/8.80 apply (zenon_L560_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hfe | zenon_intro zenon_H32a ]. % 8.61/8.80 apply (zenon_L394_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H108 | zenon_intro zenon_H32b ]. % 8.61/8.80 apply (zenon_L471_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H3c | zenon_intro zenon_He8 ]. % 8.61/8.80 apply (zenon_L6_); trivial. % 8.61/8.80 apply (zenon_L474_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.61/8.80 apply (zenon_L558_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.61/8.80 apply (zenon_L559_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.61/8.80 apply (zenon_L560_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.61/8.80 apply (zenon_L250_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.61/8.80 apply (zenon_L103_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.61/8.80 apply (zenon_L396_); trivial. % 8.61/8.80 apply (zenon_L563_); trivial. % 8.61/8.80 apply (zenon_L201_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.61/8.80 apply (zenon_L527_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2a4); [ zenon_intro zenon_H26f | zenon_intro zenon_H2ad ]. % 8.61/8.80 apply (zenon_L461_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H274 | zenon_intro zenon_H2ae ]. % 8.61/8.80 apply (zenon_L557_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H276 | zenon_intro zenon_H103 ]. % 8.61/8.80 apply (zenon_L245_); trivial. % 8.61/8.80 apply (zenon_L201_); trivial. % 8.61/8.80 apply (zenon_L343_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2a4); [ zenon_intro zenon_H26f | zenon_intro zenon_H2ad ]. % 8.61/8.80 apply (zenon_L461_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H274 | zenon_intro zenon_H2ae ]. % 8.61/8.80 apply (zenon_L557_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H276 | zenon_intro zenon_H103 ]. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.61/8.80 apply (zenon_L527_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.61/8.80 apply (zenon_L20_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.61/8.80 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.61/8.80 apply (zenon_L558_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.61/8.80 apply (zenon_L559_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.61/8.80 apply (zenon_L566_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_H24 | zenon_intro zenon_Hc6 ]. % 8.61/8.80 apply (zenon_L341_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Had | zenon_intro zenon_Hc7 ]. % 8.61/8.80 apply (zenon_L569_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H80 | zenon_intro zenon_Hc3 ]. % 8.61/8.80 apply (zenon_L40_); trivial. % 8.61/8.80 apply (zenon_L111_); trivial. % 8.61/8.80 apply (zenon_L570_); trivial. % 8.61/8.80 apply (zenon_L123_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.61/8.80 apply (zenon_L527_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.61/8.80 apply (zenon_L571_); trivial. % 8.61/8.80 apply (zenon_L343_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H41. zenon_intro zenon_H4a. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H4a). zenon_intro zenon_H154. zenon_intro zenon_H2c3. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.61/8.80 apply (zenon_L4_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.61/8.80 apply (zenon_L499_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H35d); [ zenon_intro zenon_Hac | zenon_intro zenon_H35f ]. % 8.61/8.80 apply (zenon_L499_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_H358 | zenon_intro zenon_H360 ]. % 8.61/8.80 apply (zenon_L572_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Had | zenon_intro zenon_Hd1 ]. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.61/8.80 apply (zenon_L73_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.61/8.80 apply (zenon_L572_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.61/8.80 apply (zenon_L249_); trivial. % 8.61/8.80 apply (zenon_L576_); trivial. % 8.61/8.80 apply (zenon_L47_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.61/8.80 apply (zenon_L558_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.61/8.80 apply (zenon_L559_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.61/8.80 apply (zenon_L566_); trivial. % 8.61/8.80 apply (zenon_L544_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.61/8.80 apply (zenon_L13_); trivial. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H59. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.61/8.80 apply (zenon_L193_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.61/8.80 apply (zenon_L194_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.61/8.80 apply (zenon_L116_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.61/8.80 apply (zenon_L417_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.61/8.80 apply (zenon_L514_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.61/8.80 apply (zenon_L515_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.61/8.80 apply (zenon_L460_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.61/8.80 apply (zenon_L333_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.61/8.80 apply (zenon_L129_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.61/8.80 apply (zenon_L577_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.61/8.80 apply (zenon_L578_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.61/8.80 apply (zenon_L296_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.61/8.80 apply (zenon_L202_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.61/8.80 apply (zenon_L459_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.61/8.80 apply (zenon_L443_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.61/8.80 apply (zenon_L444_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.61/8.80 apply (zenon_L579_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.61/8.80 apply (zenon_L520_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.61/8.80 apply (zenon_L580_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.61/8.80 apply (zenon_L419_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.61/8.80 apply (zenon_L522_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.61/8.80 apply (zenon_L523_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.61/8.80 apply (zenon_L146_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.61/8.80 apply (zenon_L334_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.61/8.80 apply (zenon_L581_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.61/8.80 apply (zenon_L151_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H1cc). zenon_intro zenon_H29. zenon_intro zenon_H1cd. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H1cd). zenon_intro zenon_H15a. zenon_intro zenon_H1a5. % 8.61/8.80 apply (zenon_L582_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.61/8.80 apply (zenon_L297_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.61/8.80 apply (zenon_L298_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.61/8.80 apply (zenon_L356_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.61/8.80 apply (zenon_L446_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.61/8.80 apply (zenon_L447_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.61/8.80 apply (zenon_L464_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.61/8.80 apply (zenon_L465_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.61/8.80 apply (zenon_L188_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.61/8.80 apply (zenon_L422_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.61/8.80 apply (zenon_L583_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.61/8.80 apply (zenon_L529_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.61/8.80 apply (zenon_L364_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.61/8.80 apply (zenon_L335_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.61/8.80 apply (zenon_L241_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.61/8.80 apply (zenon_L242_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.61/8.80 apply (zenon_L4_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.61/8.80 apply (zenon_L499_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.61/8.80 apply (zenon_L261_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.61/8.80 apply (zenon_L582_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.61/8.80 apply (zenon_L396_); trivial. % 8.61/8.80 apply (zenon_L590_); trivial. % 8.61/8.80 apply (zenon_L416_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.61/8.80 apply (zenon_L299_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.61/8.80 apply (zenon_L457_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.61/8.80 apply (zenon_L423_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.61/8.80 apply (zenon_L451_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.61/8.80 apply (zenon_L452_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.61/8.80 apply (zenon_L223_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.61/8.80 apply (zenon_L224_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.61/8.80 apply (zenon_L225_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.61/8.80 apply (zenon_L372_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H215). zenon_intro zenon_H1b1. zenon_intro zenon_H216. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H216). zenon_intro zenon_Hb3. zenon_intro zenon_H183. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H183). zenon_intro zenon_H6b. zenon_intro zenon_H73. % 8.61/8.80 apply (zenon_L591_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.61/8.80 apply (zenon_L539_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.61/8.80 apply (zenon_L482_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.61/8.80 apply (zenon_L378_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.61/8.80 apply (zenon_L453_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.61/8.80 apply (zenon_L592_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.61/8.80 apply (zenon_L542_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.61/8.80 apply (zenon_L382_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.61/8.80 apply (zenon_L383_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.61/8.80 apply (zenon_L385_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.61/8.80 apply (zenon_L454_); trivial. % 8.61/8.80 apply (zenon_L455_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.61/8.80 apply (zenon_L119_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.61/8.80 apply (zenon_L6_); trivial. % 8.61/8.80 apply (zenon_L384_); trivial. % 8.61/8.80 apply (zenon_L375_); trivial. % 8.61/8.80 (* end of lemma zenon_L593_ *) % 8.61/8.80 assert (zenon_L594_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((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))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (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)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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 (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.61/8.80 do 0 intro. intros zenon_H207 zenon_H2f8 zenon_H34d zenon_H105 zenon_He4 zenon_H2bf zenon_H2e2 zenon_Hf8 zenon_H2a3 zenon_H36 zenon_H124 zenon_H11f zenon_Hf9 zenon_H285 zenon_H27f zenon_H282 zenon_H150 zenon_Hb7 zenon_H2c9 zenon_H295 zenon_H1dc zenon_H2c0 zenon_H270 zenon_H1f zenon_H16d zenon_H2f3 zenon_H164 zenon_H2fc zenon_H3a zenon_H73 zenon_Hb4 zenon_H2e8 zenon_H2a4 zenon_H1dd zenon_H336 zenon_H2a1 zenon_H137 zenon_H2df zenon_H9a zenon_H300 zenon_H90 zenon_H134 zenon_Hf3 zenon_Hba zenon_H35d zenon_H35e zenon_H6c zenon_H12b zenon_H129 zenon_H2a5 zenon_H32e zenon_H10c zenon_H145 zenon_H2d4 zenon_H2d2 zenon_H29f zenon_Hc5 zenon_H170 zenon_H153 zenon_H22e zenon_H25 zenon_Hab zenon_H2b zenon_H22d zenon_H127 zenon_H173 zenon_H331 zenon_Hd0 zenon_H2b5 zenon_H1d3 zenon_Hc2 zenon_H303 zenon_H329 zenon_H78 zenon_H7d zenon_H19a zenon_H192 zenon_H109 zenon_He7 zenon_Hff zenon_H2d8 zenon_H169 zenon_H31 zenon_H2a2 zenon_H74 zenon_H197 zenon_H67 zenon_H2b8 zenon_Ha3 zenon_H1f6 zenon_Ha8 zenon_H1d7 zenon_H1d9. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H207). zenon_intro zenon_H3c. zenon_intro zenon_H208. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H208). zenon_intro zenon_Hbd. zenon_intro zenon_H1b0. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb3. zenon_intro zenon_H1b1. % 8.61/8.80 apply (zenon_L593_); trivial. % 8.61/8.80 (* end of lemma zenon_L594_ *) % 8.61/8.80 assert (zenon_L595_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> False). % 8.61/8.80 do 0 intro. intros zenon_H221 zenon_H3a zenon_H3c. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H221). zenon_intro zenon_H98. zenon_intro zenon_H222. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H222). zenon_intro zenon_H195. zenon_intro zenon_H1a5. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H1a5). zenon_intro zenon_H3b. zenon_intro zenon_H3b. % 8.61/8.80 apply (zenon_L6_); trivial. % 8.61/8.80 (* end of lemma zenon_L595_ *) % 8.61/8.80 assert (zenon_L596_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 8.61/8.80 do 0 intro. intros zenon_H21d zenon_H3c zenon_H12b. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H98. zenon_intro zenon_H21e. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H21e). zenon_intro zenon_H195. zenon_intro zenon_H19f. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H19f). zenon_intro zenon_H7e. zenon_intro zenon_Hc8. % 8.61/8.80 apply (zenon_L75_); trivial. % 8.61/8.80 (* end of lemma zenon_L596_ *) % 8.61/8.80 assert (zenon_L597_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> False). % 8.61/8.80 do 0 intro. intros zenon_H21f zenon_H154. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H21f). zenon_intro zenon_H98. zenon_intro zenon_H220. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H220). zenon_intro zenon_H195. zenon_intro zenon_H1a2. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H1a2). zenon_intro zenon_H93. zenon_intro zenon_H191. % 8.61/8.80 apply (zenon_L97_); trivial. % 8.61/8.80 (* end of lemma zenon_L597_ *) % 8.61/8.80 assert (zenon_L598_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((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) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.61/8.80 do 0 intro. intros zenon_H1f0 zenon_H90 zenon_H300 zenon_H2f8 zenon_H134 zenon_H336 zenon_H94 zenon_Heb zenon_H11e zenon_H331 zenon_Hba zenon_H303 zenon_Hbf zenon_He4 zenon_H322 zenon_H105 zenon_H1d3 zenon_H2df zenon_H2f3 zenon_Hd0 zenon_H16d zenon_H1f zenon_H270 zenon_H2a4 zenon_H2b5 zenon_H2c0 zenon_H169 zenon_H1dc zenon_H2a1 zenon_H295 zenon_H19a zenon_H2c9 zenon_Hb7 zenon_H6c zenon_H74 zenon_H150 zenon_H282 zenon_H137 zenon_H27f zenon_H2e8 zenon_H285 zenon_Hf3 zenon_Hf9 zenon_H2a3 zenon_Hf8 zenon_H164 zenon_H1dd zenon_H2e2 zenon_H2bf zenon_H124 zenon_H11f zenon_H36 zenon_H2fc zenon_H12b zenon_H129 zenon_H2a5 zenon_H329 zenon_H2d8 zenon_Hff zenon_He7 zenon_H109 zenon_H32e zenon_Hb4 zenon_H10c zenon_H145 zenon_H2d4 zenon_H2d2 zenon_H29f zenon_H2a2 zenon_H3a zenon_Hc5 zenon_H170 zenon_H153 zenon_H22e zenon_H25 zenon_H31 zenon_H127 zenon_H78 zenon_H7d zenon_H1f6 zenon_Hc2 zenon_Hab zenon_H2b zenon_H197 zenon_H67 zenon_H2b8 zenon_Ha3 zenon_H192 zenon_Ha8 zenon_H1d7 zenon_H22d zenon_H173 zenon_H1d9. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_Hc8. zenon_intro zenon_H1f1. % 8.61/8.80 apply (zenon_L495_); trivial. % 8.61/8.80 (* end of lemma zenon_L598_ *) % 8.61/8.80 assert (zenon_L599_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> False). % 8.61/8.80 do 0 intro. intros zenon_H1f2 zenon_H1d zenon_H67. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H1f2). zenon_intro zenon_H191. zenon_intro zenon_H1f3. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H93. zenon_intro zenon_H183. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H183). zenon_intro zenon_H6b. zenon_intro zenon_H73. % 8.61/8.80 apply (zenon_L77_); trivial. % 8.61/8.80 (* end of lemma zenon_L599_ *) % 8.61/8.80 assert (zenon_L600_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.61/8.80 do 0 intro. intros zenon_H215 zenon_H1d9 zenon_H98. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H215). zenon_intro zenon_H1b1. zenon_intro zenon_H216. % 8.61/8.80 apply (zenon_L375_); trivial. % 8.61/8.80 (* end of lemma zenon_L600_ *) % 8.61/8.80 assert (zenon_L601_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2))))) -> (~((op (e2) (op (e2) (e3))) = (e3))) -> False). % 8.61/8.80 do 0 intro. intros zenon_H21f zenon_H57. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H21f). zenon_intro zenon_H98. zenon_intro zenon_H220. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H220). zenon_intro zenon_H195. zenon_intro zenon_H1a2. % 8.61/8.80 apply (zenon_L409_); trivial. % 8.61/8.80 (* end of lemma zenon_L601_ *) % 8.61/8.80 assert (zenon_L602_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((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) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.61/8.80 do 0 intro. intros zenon_H2fc zenon_H1d7 zenon_Ha8 zenon_H3a zenon_H197 zenon_H12b zenon_Ha3 zenon_H73 zenon_Hab zenon_H1d9 zenon_Hc2 zenon_H1d zenon_H124 zenon_H2bf zenon_H1dc zenon_H1dd zenon_H169 zenon_H2c0 zenon_H2b8 zenon_H2b5 zenon_H109 zenon_H22e zenon_H31 zenon_H2b zenon_H7d zenon_H129 zenon_H1f6 zenon_H2a5 zenon_H2a4 zenon_H270 zenon_H1d3 zenon_Hb7 zenon_H78 zenon_H192 zenon_H145 zenon_H285 zenon_H295 zenon_H2a3 zenon_Hb4 zenon_H25 zenon_H150 zenon_H1f zenon_H2a2 zenon_H2a1 zenon_H282 zenon_H137 zenon_H173 zenon_H27f zenon_H127 zenon_H11f zenon_H67 zenon_H16d zenon_H29f zenon_Hf9 zenon_Hd0 zenon_H22d zenon_H170 zenon_H74 zenon_H6c zenon_H322 zenon_Hbf zenon_H11e zenon_H94 zenon_H2d8 zenon_Hff zenon_He7 zenon_H19a zenon_H329 zenon_H303 zenon_H331 zenon_H153 zenon_Hc5 zenon_H2d2 zenon_H2d4 zenon_H10c zenon_H32e zenon_H35e zenon_H35d zenon_Hba zenon_Hf3 zenon_H134 zenon_H90 zenon_H300 zenon_H9a zenon_H2df zenon_H336 zenon_H2e8 zenon_H164 zenon_H2f3 zenon_H2c9 zenon_H36 zenon_Hf8 zenon_H2e2 zenon_He4 zenon_H105 zenon_H34d zenon_H2f8 zenon_Heb zenon_H98. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.61/8.80 apply (zenon_L73_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.61/8.80 apply (zenon_L119_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H118. zenon_intro zenon_H18a. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.61/8.80 apply (zenon_L113_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.61/8.80 apply (zenon_L114_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.61/8.80 apply (zenon_L116_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.61/8.80 apply (zenon_L118_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.61/8.80 apply (zenon_L514_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.61/8.80 apply (zenon_L515_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.61/8.80 apply (zenon_L516_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.61/8.80 apply (zenon_L517_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.61/8.80 apply (zenon_L129_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.61/8.80 apply (zenon_L518_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.61/8.80 apply (zenon_L163_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.61/8.80 apply (zenon_L164_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.61/8.80 apply (zenon_L135_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.61/8.80 apply (zenon_L519_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.61/8.80 apply (zenon_L137_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.61/8.80 apply (zenon_L138_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.61/8.80 apply (zenon_L139_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.61/8.80 apply (zenon_L520_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.61/8.80 apply (zenon_L521_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.61/8.80 apply (zenon_L142_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.61/8.80 apply (zenon_L522_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.61/8.80 apply (zenon_L523_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.61/8.80 apply (zenon_L146_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.61/8.80 apply (zenon_L524_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.61/8.80 apply (zenon_L148_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.61/8.80 apply (zenon_L151_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.61/8.80 apply (zenon_L179_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.61/8.80 apply (zenon_L525_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.61/8.80 apply (zenon_L355_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.61/8.80 apply (zenon_L356_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.61/8.80 apply (zenon_L526_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.61/8.80 apply (zenon_L357_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.61/8.80 apply (zenon_L186_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.61/8.80 apply (zenon_L187_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.61/8.80 apply (zenon_L188_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.61/8.80 apply (zenon_L361_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.61/8.80 apply (zenon_L528_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.61/8.80 apply (zenon_L529_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.61/8.80 apply (zenon_L364_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.61/8.80 apply (zenon_L530_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.61/8.80 apply (zenon_L241_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.61/8.80 apply (zenon_L242_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.61/8.80 apply (zenon_L531_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.61/8.80 apply (zenon_L272_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.61/8.80 apply (zenon_L273_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.61/8.80 apply (zenon_L594_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.61/8.80 apply (zenon_L369_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.61/8.80 apply (zenon_L370_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.61/8.80 apply (zenon_L274_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.61/8.80 apply (zenon_L275_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.61/8.80 apply (zenon_L537_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.61/8.80 apply (zenon_L373_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.61/8.80 apply (zenon_L538_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.61/8.80 apply (zenon_L539_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.61/8.80 apply (zenon_L540_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.61/8.80 apply (zenon_L378_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.61/8.80 apply (zenon_L379_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.61/8.80 apply (zenon_L541_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.61/8.80 apply (zenon_L595_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.61/8.80 apply (zenon_L382_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.61/8.80 apply (zenon_L383_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.61/8.80 apply (zenon_L386_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.61/8.80 apply (zenon_L387_); trivial. % 8.61/8.80 apply (zenon_L388_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H41. zenon_intro zenon_H4a. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H4a). zenon_intro zenon_H154. zenon_intro zenon_H2c3. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.61/8.80 apply (zenon_L113_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.61/8.80 apply (zenon_L114_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.61/8.80 apply (zenon_L116_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.61/8.80 apply (zenon_L118_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.61/8.80 apply (zenon_L514_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.61/8.80 apply (zenon_L515_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.61/8.80 apply (zenon_L277_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.61/8.80 apply (zenon_L389_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.61/8.80 apply (zenon_L160_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.61/8.80 apply (zenon_L278_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.61/8.80 apply (zenon_L163_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.61/8.80 apply (zenon_L164_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.61/8.80 apply (zenon_L135_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.61/8.80 apply (zenon_L546_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.61/8.80 apply (zenon_L137_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.61/8.80 apply (zenon_L138_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.61/8.80 apply (zenon_L139_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.61/8.80 apply (zenon_L140_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.61/8.80 apply (zenon_L521_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.61/8.80 apply (zenon_L142_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.61/8.80 apply (zenon_L522_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.61/8.80 apply (zenon_L523_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.61/8.80 apply (zenon_L146_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.61/8.80 apply (zenon_L524_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.61/8.80 apply (zenon_L178_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.61/8.80 apply (zenon_L151_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.61/8.80 apply (zenon_L179_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.61/8.80 apply (zenon_L525_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.61/8.80 apply (zenon_L355_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.61/8.80 apply (zenon_L356_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.61/8.80 apply (zenon_L526_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.61/8.80 apply (zenon_L357_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.61/8.80 apply (zenon_L186_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.61/8.80 apply (zenon_L187_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.61/8.80 apply (zenon_L188_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.61/8.80 apply (zenon_L406_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.61/8.80 apply (zenon_L547_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.61/8.80 apply (zenon_L192_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.61/8.80 apply (zenon_L364_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.61/8.80 apply (zenon_L279_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.61/8.80 apply (zenon_L241_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.61/8.80 apply (zenon_L242_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.61/8.80 apply (zenon_L531_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.61/8.80 apply (zenon_L272_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.61/8.80 apply (zenon_L407_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.61/8.80 apply (zenon_L548_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.61/8.80 apply (zenon_L369_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.61/8.80 apply (zenon_L370_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.61/8.80 apply (zenon_L274_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.61/8.80 apply (zenon_L281_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.61/8.80 apply (zenon_L276_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.61/8.80 apply (zenon_L373_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.61/8.80 apply (zenon_L549_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.61/8.80 apply (zenon_L376_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.61/8.80 apply (zenon_L540_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.61/8.80 apply (zenon_L378_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.61/8.80 apply (zenon_L596_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.61/8.80 apply (zenon_L597_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.61/8.80 apply (zenon_L595_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.61/8.80 apply (zenon_L382_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.61/8.80 apply (zenon_L383_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.61/8.80 apply (zenon_L386_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.61/8.80 apply (zenon_L387_); trivial. % 8.61/8.80 apply (zenon_L388_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H4c. zenon_intro zenon_H57. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.61/8.80 apply (zenon_L113_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.61/8.80 apply (zenon_L114_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.61/8.80 apply (zenon_L282_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.61/8.80 apply (zenon_L118_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.61/8.80 apply (zenon_L514_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.61/8.80 apply (zenon_L515_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.61/8.80 apply (zenon_L283_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.61/8.80 apply (zenon_L517_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.61/8.80 apply (zenon_L129_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.61/8.80 apply (zenon_L284_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.61/8.80 apply (zenon_L163_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.61/8.80 apply (zenon_L285_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.61/8.80 apply (zenon_L135_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.61/8.80 apply (zenon_L519_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.61/8.80 apply (zenon_L410_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.61/8.80 apply (zenon_L138_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.61/8.80 apply (zenon_L139_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.61/8.80 apply (zenon_L520_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.61/8.80 apply (zenon_L286_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.61/8.80 apply (zenon_L142_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.61/8.80 apply (zenon_L522_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.61/8.80 apply (zenon_L523_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.61/8.80 apply (zenon_L146_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.61/8.80 apply (zenon_L524_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.61/8.80 apply (zenon_L411_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.61/8.80 apply (zenon_L151_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.61/8.80 apply (zenon_L179_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.61/8.80 apply (zenon_L287_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.61/8.80 apply (zenon_L355_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.61/8.80 apply (zenon_L356_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.61/8.80 apply (zenon_L412_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.61/8.80 apply (zenon_L357_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.61/8.80 apply (zenon_L186_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.61/8.80 apply (zenon_L187_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.61/8.80 apply (zenon_L188_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.61/8.80 apply (zenon_L598_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.61/8.80 apply (zenon_L599_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.61/8.80 apply (zenon_L529_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.61/8.80 apply (zenon_L364_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.61/8.80 apply (zenon_L530_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.61/8.80 apply (zenon_L241_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.61/8.80 apply (zenon_L242_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.61/8.80 apply (zenon_L531_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.61/8.80 apply (zenon_L272_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.61/8.80 apply (zenon_L407_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.61/8.80 apply (zenon_L594_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.61/8.80 apply (zenon_L369_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.61/8.80 apply (zenon_L370_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.61/8.80 apply (zenon_L274_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.61/8.80 apply (zenon_L413_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.61/8.80 apply (zenon_L293_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.61/8.80 apply (zenon_L373_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.61/8.80 apply (zenon_L600_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.61/8.80 apply (zenon_L539_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.61/8.80 apply (zenon_L414_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.61/8.80 apply (zenon_L378_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.61/8.80 apply (zenon_L415_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.61/8.80 apply (zenon_L601_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.61/8.80 apply (zenon_L595_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.61/8.80 apply (zenon_L382_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.61/8.80 apply (zenon_L383_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.61/8.80 apply (zenon_L386_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.61/8.80 apply (zenon_L387_); trivial. % 8.61/8.80 apply (zenon_L388_); trivial. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 8.61/8.80 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H59. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.61/8.80 apply (zenon_L113_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.61/8.80 apply (zenon_L114_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.61/8.80 apply (zenon_L116_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.61/8.80 apply (zenon_L417_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.61/8.80 apply (zenon_L514_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.61/8.80 apply (zenon_L515_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.61/8.80 apply (zenon_L516_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.61/8.80 apply (zenon_L333_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.61/8.80 apply (zenon_L160_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.61/8.80 apply (zenon_L518_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.61/8.80 apply (zenon_L163_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.61/8.80 apply (zenon_L296_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.61/8.80 apply (zenon_L135_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.61/8.80 apply (zenon_L459_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.61/8.80 apply (zenon_L418_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.61/8.80 apply (zenon_L138_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.61/8.80 apply (zenon_L139_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.61/8.80 apply (zenon_L140_); trivial. % 8.61/8.80 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.61/8.80 apply (zenon_L521_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.61/8.81 apply (zenon_L419_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.61/8.81 apply (zenon_L522_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.61/8.81 apply (zenon_L523_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.61/8.81 apply (zenon_L146_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.61/8.81 apply (zenon_L334_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.61/8.81 apply (zenon_L178_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.61/8.81 apply (zenon_L151_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.61/8.81 apply (zenon_L179_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.61/8.81 apply (zenon_L297_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.61/8.81 apply (zenon_L298_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.61/8.81 apply (zenon_L356_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.61/8.81 apply (zenon_L421_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.61/8.81 apply (zenon_L357_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.61/8.81 apply (zenon_L186_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.61/8.81 apply (zenon_L187_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.61/8.81 apply (zenon_L188_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.61/8.81 apply (zenon_L422_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.61/8.81 apply (zenon_L599_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.61/8.81 apply (zenon_L192_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.61/8.81 apply (zenon_L364_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.61/8.81 apply (zenon_L335_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.61/8.81 apply (zenon_L241_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.61/8.81 apply (zenon_L242_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.61/8.81 apply (zenon_L531_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.61/8.81 apply (zenon_L299_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.61/8.81 apply (zenon_L300_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.61/8.81 apply (zenon_L423_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.61/8.81 apply (zenon_L369_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.61/8.81 apply (zenon_L370_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.61/8.81 apply (zenon_L274_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.61/8.81 apply (zenon_L413_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.61/8.81 apply (zenon_L276_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.61/8.81 apply (zenon_L373_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.61/8.81 apply (zenon_L600_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.61/8.81 apply (zenon_L376_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.61/8.81 apply (zenon_L540_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.61/8.81 apply (zenon_L378_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.61/8.81 apply (zenon_L596_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.61/8.81 apply (zenon_L541_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.61/8.81 apply (zenon_L595_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.61/8.81 apply (zenon_L382_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.61/8.81 apply (zenon_L383_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.61/8.81 apply (zenon_L386_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.61/8.81 apply (zenon_L387_); trivial. % 8.61/8.81 apply (zenon_L388_); trivial. % 8.61/8.81 apply (zenon_L53_); trivial. % 8.61/8.81 (* end of lemma zenon_L602_ *) % 8.61/8.81 assert (zenon_L603_ : ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((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) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 8.61/8.81 do 0 intro. intros zenon_Hcc zenon_H196 zenon_Hf4 zenon_H3b zenon_H2fc zenon_H1d7 zenon_Ha8 zenon_H3a zenon_H197 zenon_H12b zenon_Ha3 zenon_H73 zenon_Hab zenon_H1d9 zenon_Hc2 zenon_H1d zenon_H124 zenon_H2bf zenon_H1dc zenon_H1dd zenon_H169 zenon_H2c0 zenon_H2b8 zenon_H2b5 zenon_H109 zenon_H22e zenon_H31 zenon_H2b zenon_H7d zenon_H129 zenon_H1f6 zenon_H2a5 zenon_H2a4 zenon_H270 zenon_H1d3 zenon_Hb7 zenon_H78 zenon_H192 zenon_H145 zenon_H285 zenon_H295 zenon_H2a3 zenon_Hb4 zenon_H25 zenon_H150 zenon_H1f zenon_H2a2 zenon_H2a1 zenon_H282 zenon_H137 zenon_H173 zenon_H27f zenon_H127 zenon_H11f zenon_H67 zenon_H16d zenon_H29f zenon_Hf9 zenon_Hd0 zenon_H22d zenon_H170 zenon_H74 zenon_H6c zenon_H322 zenon_Hbf zenon_H11e zenon_H94 zenon_H2d8 zenon_Hff zenon_He7 zenon_H19a zenon_H329 zenon_H303 zenon_H331 zenon_H153 zenon_Hc5 zenon_H2d2 zenon_H2d4 zenon_H10c zenon_H32e zenon_H35e zenon_H35d zenon_Hba zenon_Hf3 zenon_H134 zenon_H90 zenon_H300 zenon_H9a zenon_H2df zenon_H336 zenon_H2e8 zenon_H164 zenon_H2f3 zenon_H2c9 zenon_H36 zenon_Hf8 zenon_H2e2 zenon_He4 zenon_H105 zenon_H34d zenon_H2f8 zenon_Heb. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H2d5 ]. % 8.61/8.81 apply (zenon_L512_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H2d6 ]. % 8.61/8.81 apply (zenon_L319_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_Hbd | zenon_intro zenon_H98 ]. % 8.61/8.81 apply (zenon_L513_); trivial. % 8.61/8.81 apply (zenon_L602_); trivial. % 8.61/8.81 (* end of lemma zenon_L603_ *) % 8.61/8.81 assert (zenon_L604_ : ((op (e2) (e0)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((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) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 8.61/8.81 do 0 intro. intros zenon_H143 zenon_Hcc zenon_Hf4 zenon_H3b zenon_H2fc zenon_H1d7 zenon_Ha8 zenon_H3a zenon_H197 zenon_H12b zenon_Ha3 zenon_H73 zenon_Hab zenon_H1d9 zenon_Hc2 zenon_H1d zenon_H124 zenon_H2bf zenon_H1dc zenon_H1dd zenon_H169 zenon_H2c0 zenon_H2b8 zenon_H2b5 zenon_H109 zenon_H22e zenon_H31 zenon_H2b zenon_H7d zenon_H129 zenon_H1f6 zenon_H2a5 zenon_H2a4 zenon_H270 zenon_H1d3 zenon_Hb7 zenon_H78 zenon_H192 zenon_H145 zenon_H285 zenon_H295 zenon_H2a3 zenon_Hb4 zenon_H25 zenon_H150 zenon_H1f zenon_H2a2 zenon_H2a1 zenon_H282 zenon_H137 zenon_H173 zenon_H27f zenon_H127 zenon_H11f zenon_H67 zenon_H16d zenon_H29f zenon_Hf9 zenon_Hd0 zenon_H22d zenon_H170 zenon_H74 zenon_H6c zenon_H322 zenon_Hbf zenon_H11e zenon_H94 zenon_H2d8 zenon_Hff zenon_He7 zenon_H19a zenon_H329 zenon_H303 zenon_H331 zenon_H153 zenon_Hc5 zenon_H2d2 zenon_H2d4 zenon_H10c zenon_H32e zenon_H35e zenon_H35d zenon_Hba zenon_Hf3 zenon_H134 zenon_H90 zenon_H300 zenon_H9a zenon_H2df zenon_H336 zenon_H2e8 zenon_H164 zenon_H2f3 zenon_H2c9 zenon_H36 zenon_Hf8 zenon_H2e2 zenon_He4 zenon_H105 zenon_H34d zenon_H2f8 zenon_Heb. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.61/8.81 apply (zenon_L261_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.61/8.81 apply (zenon_L103_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.61/8.81 apply (zenon_L396_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H165 | zenon_intro zenon_H19b ]. % 8.61/8.81 apply (zenon_L101_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H15a | zenon_intro zenon_H19c ]. % 8.61/8.81 apply (zenon_L472_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H191 | zenon_intro zenon_H196 ]. % 8.61/8.81 apply (zenon_L509_); trivial. % 8.61/8.81 apply (zenon_L603_); trivial. % 8.61/8.81 (* end of lemma zenon_L604_ *) % 8.61/8.81 assert (zenon_L605_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 8.61/8.81 do 0 intro. intros zenon_H11f zenon_H1d zenon_H127 zenon_H105 zenon_H16b zenon_Hff zenon_H108 zenon_Hd0 zenon_H5a zenon_He4. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.61/8.81 apply (zenon_L73_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.61/8.81 apply (zenon_L434_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.61/8.81 apply (zenon_L108_); trivial. % 8.61/8.81 apply (zenon_L503_); trivial. % 8.61/8.81 (* end of lemma zenon_L605_ *) % 8.61/8.81 assert (zenon_L606_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 8.61/8.81 do 0 intro. intros zenon_H303 zenon_H67 zenon_H143 zenon_Hf4 zenon_H169 zenon_H3b zenon_H7d zenon_H11f zenon_H1d zenon_H127 zenon_H105 zenon_Hff zenon_H108 zenon_Hd0 zenon_H5a zenon_He4. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.61/8.81 apply (zenon_L261_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.61/8.81 apply (zenon_L103_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.61/8.81 apply (zenon_L396_); trivial. % 8.61/8.81 apply (zenon_L605_); trivial. % 8.61/8.81 (* end of lemma zenon_L606_ *) % 8.61/8.81 assert (zenon_L607_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (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 (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = 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(e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 8.61/8.81 do 0 intro. intros zenon_Heb zenon_H2f8 zenon_H34d zenon_H2e2 zenon_Hf8 zenon_H36 zenon_H2c9 zenon_H2f3 zenon_H164 zenon_H2e8 zenon_H336 zenon_H2df zenon_H9a zenon_H300 zenon_H90 zenon_H134 zenon_Hf3 zenon_Hba zenon_H35d zenon_H35e zenon_H32e zenon_H10c zenon_H2d4 zenon_H2d2 zenon_Hc5 zenon_H153 zenon_H331 zenon_H329 zenon_H19a zenon_He7 zenon_H2d8 zenon_H11e zenon_Hbf zenon_H322 zenon_H6c zenon_H74 zenon_H170 zenon_H22d zenon_Hf9 zenon_H29f zenon_H16d zenon_H27f zenon_H173 zenon_H137 zenon_H282 zenon_H2a1 zenon_H2a2 zenon_H1f zenon_H150 zenon_H25 zenon_Hb4 zenon_H2a3 zenon_H295 zenon_H285 zenon_H145 zenon_H192 zenon_H78 zenon_Hb7 zenon_H1d3 zenon_H270 zenon_H2a4 zenon_H2a5 zenon_H1f6 zenon_H129 zenon_H2b zenon_H31 zenon_H22e zenon_H109 zenon_H2b5 zenon_H2b8 zenon_H2c0 zenon_H1dd zenon_H1dc zenon_H2bf zenon_H124 zenon_Hc2 zenon_H1d9 zenon_Hab zenon_H73 zenon_Ha3 zenon_H12b zenon_H197 zenon_H3a zenon_Ha8 zenon_H1d7 zenon_H2fc zenon_H94 zenon_H303 zenon_H67 zenon_H143 zenon_Hf4 zenon_H169 zenon_H3b zenon_H7d zenon_H11f zenon_H1d zenon_H127 zenon_H105 zenon_Hff zenon_Hd0 zenon_H5a zenon_He4. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.61/8.81 apply (zenon_L508_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.61/8.81 apply (zenon_L604_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.61/8.81 apply (zenon_L28_); trivial. % 8.61/8.81 apply (zenon_L606_); trivial. % 8.61/8.81 (* end of lemma zenon_L607_ *) % 8.61/8.81 assert (zenon_L608_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 8.61/8.81 do 0 intro. intros zenon_H2d8 zenon_He4 zenon_Hd0 zenon_Hff zenon_Hd1 zenon_H105 zenon_H109 zenon_H108 zenon_H5a zenon_He7. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H2d9 ]. % 8.61/8.81 apply (zenon_L500_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2d9); [ zenon_intro zenon_H16b | zenon_intro zenon_H2da ]. % 8.61/8.81 apply (zenon_L434_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H3c | zenon_intro zenon_H195 ]. % 8.61/8.81 apply (zenon_L63_); trivial. % 8.61/8.81 apply (zenon_L501_); trivial. % 8.61/8.81 (* end of lemma zenon_L608_ *) % 8.61/8.81 assert (zenon_L609_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 8.61/8.81 do 0 intro. intros zenon_H329 zenon_H7d zenon_Hd6 zenon_He7 zenon_H109 zenon_H105 zenon_Hd1 zenon_Hff zenon_Hd0 zenon_He4 zenon_H2d8 zenon_H3b zenon_H3a zenon_Ha8 zenon_H5a. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hfe | zenon_intro zenon_H32a ]. % 8.61/8.81 apply (zenon_L81_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H108 | zenon_intro zenon_H32b ]. % 8.61/8.81 apply (zenon_L608_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H3c | zenon_intro zenon_He8 ]. % 8.61/8.81 apply (zenon_L6_); trivial. % 8.61/8.81 apply (zenon_L439_); trivial. % 8.61/8.81 (* end of lemma zenon_L609_ *) % 8.61/8.81 assert (zenon_L610_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 8.61/8.81 do 0 intro. intros zenon_H11f zenon_H1d zenon_H127 zenon_H109 zenon_H329 zenon_H7d zenon_Hd6 zenon_He7 zenon_H105 zenon_Hff zenon_Hd0 zenon_He4 zenon_H12b zenon_H143 zenon_H2d8 zenon_H3b zenon_H3a zenon_Ha8 zenon_H5a. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.61/8.81 apply (zenon_L73_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.61/8.81 apply (zenon_L609_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.61/8.81 apply (zenon_L253_); trivial. % 8.61/8.81 apply (zenon_L505_); trivial. % 8.61/8.81 (* end of lemma zenon_L610_ *) % 8.61/8.81 assert (zenon_L611_ : (~((op (op (e0) (e0)) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> False). % 8.61/8.81 do 0 intro. intros zenon_H363 zenon_H77. % 8.61/8.81 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.61/8.81 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 8.61/8.81 congruence. % 8.61/8.81 exact (zenon_H7b zenon_H77). % 8.61/8.81 apply zenon_H3f. apply refl_equal. % 8.61/8.81 (* end of lemma zenon_L611_ *) % 8.61/8.81 assert (zenon_L612_ : ((op (e2) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> (~((e3) = (op (op (e0) (e0)) (e0)))) -> False). % 8.61/8.81 do 0 intro. intros zenon_H27e zenon_H77 zenon_H31a. % 8.61/8.81 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H28a | zenon_intro zenon_H28b ]. % 8.61/8.81 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e3) = (op (op (e0) (e0)) (e0)))). % 8.61/8.81 intro zenon_D_pnotp. % 8.61/8.81 apply zenon_H31a. % 8.61/8.81 rewrite <- zenon_D_pnotp. % 8.61/8.81 exact zenon_H28a. % 8.61/8.81 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H28b]. % 8.61/8.81 cut (((op (op (e0) (e0)) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H31b]. % 8.61/8.81 congruence. % 8.61/8.81 cut (((op (e2) (e0)) = (e3)) = ((op (op (e0) (e0)) (e0)) = (e3))). % 8.61/8.81 intro zenon_D_pnotp. % 8.61/8.81 apply zenon_H31b. % 8.61/8.81 rewrite <- zenon_D_pnotp. % 8.61/8.81 exact zenon_H27e. % 8.61/8.81 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.61/8.81 cut (((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H364]. % 8.61/8.81 congruence. % 8.61/8.81 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H28a | zenon_intro zenon_H28b ]. % 8.61/8.81 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))). % 8.61/8.81 intro zenon_D_pnotp. % 8.61/8.81 apply zenon_H364. % 8.61/8.81 rewrite <- zenon_D_pnotp. % 8.61/8.81 exact zenon_H28a. % 8.61/8.81 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H28b]. % 8.61/8.81 cut (((op (op (e0) (e0)) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H363]. % 8.61/8.81 congruence. % 8.61/8.81 apply (zenon_L611_); trivial. % 8.61/8.81 apply zenon_H28b. apply refl_equal. % 8.61/8.81 apply zenon_H28b. apply refl_equal. % 8.61/8.81 apply zenon_H58. apply refl_equal. % 8.61/8.81 apply zenon_H28b. apply refl_equal. % 8.61/8.81 apply zenon_H28b. apply refl_equal. % 8.61/8.81 (* end of lemma zenon_L612_ *) % 8.61/8.81 assert (zenon_L613_ : ((op (e3) (e2)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> False). % 8.61/8.81 do 0 intro. intros zenon_Hf6 zenon_H27e zenon_H77. % 8.61/8.81 apply (zenon_notand_s _ _ ax18); [ zenon_intro zenon_H13b | zenon_intro zenon_H365 ]. % 8.61/8.81 apply zenon_H13b. apply sym_equal. exact zenon_H77. % 8.61/8.81 apply (zenon_notand_s _ _ zenon_H365); [ zenon_intro zenon_H366 | zenon_intro zenon_H31a ]. % 8.61/8.81 elim (classic ((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H290 | zenon_intro zenon_H291 ]. % 8.61/8.81 cut (((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0)))) = ((e1) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))). % 8.61/8.81 intro zenon_D_pnotp. % 8.61/8.81 apply zenon_H366. % 8.61/8.81 rewrite <- zenon_D_pnotp. % 8.61/8.81 exact zenon_H290. % 8.61/8.81 cut (((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H291]. % 8.61/8.81 cut (((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H367]. % 8.61/8.81 congruence. % 8.61/8.81 cut (((op (e3) (e2)) = (e1)) = ((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (e1))). % 8.61/8.81 intro zenon_D_pnotp. % 8.61/8.81 apply zenon_H367. % 8.61/8.81 rewrite <- zenon_D_pnotp. % 8.61/8.81 exact zenon_Hf6. % 8.61/8.81 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.61/8.81 cut (((op (e3) (e2)) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H368]. % 8.61/8.81 congruence. % 8.61/8.81 elim (classic ((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H290 | zenon_intro zenon_H291 ]. % 8.61/8.81 cut (((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0)))) = ((op (e3) (e2)) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))). % 8.61/8.81 intro zenon_D_pnotp. % 8.61/8.81 apply zenon_H368. % 8.61/8.81 rewrite <- zenon_D_pnotp. % 8.61/8.81 exact zenon_H290. % 8.61/8.81 cut (((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (op (op (e0) (e0)) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H291]. % 8.61/8.81 cut (((op (op (op (e0) (e0)) (e0)) (op (e0) (e0))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H369]. % 8.61/8.81 congruence. % 8.61/8.81 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 8.61/8.81 cut (((op (op (e0) (e0)) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H31b]. % 8.61/8.81 congruence. % 8.61/8.81 cut (((op (e2) (e0)) = (e3)) = ((op (op (e0) (e0)) (e0)) = (e3))). % 8.61/8.81 intro zenon_D_pnotp. % 8.61/8.81 apply zenon_H31b. % 8.61/8.81 rewrite <- zenon_D_pnotp. % 8.61/8.81 exact zenon_H27e. % 8.61/8.81 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.61/8.81 cut (((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H364]. % 8.61/8.81 congruence. % 8.61/8.81 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H28a | zenon_intro zenon_H28b ]. % 8.61/8.81 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))). % 8.61/8.81 intro zenon_D_pnotp. % 8.61/8.81 apply zenon_H364. % 8.61/8.81 rewrite <- zenon_D_pnotp. % 8.61/8.81 exact zenon_H28a. % 8.61/8.81 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H28b]. % 8.61/8.81 cut (((op (op (e0) (e0)) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H363]. % 8.61/8.81 congruence. % 8.61/8.81 apply (zenon_L611_); trivial. % 8.61/8.81 apply zenon_H28b. apply refl_equal. % 8.61/8.81 apply zenon_H28b. apply refl_equal. % 8.61/8.81 apply zenon_H58. apply refl_equal. % 8.61/8.81 exact (zenon_H7b zenon_H77). % 8.61/8.81 apply zenon_H291. apply refl_equal. % 8.61/8.81 apply zenon_H291. apply refl_equal. % 8.61/8.81 apply zenon_H40. apply refl_equal. % 8.61/8.81 apply zenon_H291. apply refl_equal. % 8.61/8.81 apply zenon_H291. apply refl_equal. % 8.61/8.81 apply (zenon_L612_); trivial. % 8.61/8.81 (* end of lemma zenon_L613_ *) % 8.61/8.81 assert (zenon_L614_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> False). % 8.61/8.81 do 0 intro. intros zenon_H2df zenon_Ha3 zenon_H276 zenon_Hab zenon_H73 zenon_H3b zenon_H7d zenon_H27e zenon_H77. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.61/8.81 apply (zenon_L245_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.61/8.81 apply (zenon_L93_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.61/8.81 apply (zenon_L396_); trivial. % 8.61/8.81 apply (zenon_L613_); trivial. % 8.61/8.81 (* end of lemma zenon_L614_ *) % 8.61/8.81 assert (zenon_L615_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 8.61/8.81 do 0 intro. intros zenon_H36a zenon_H77 zenon_Hf6 zenon_Ha3 zenon_H15a zenon_Ha8 zenon_H3b zenon_H5a zenon_He7. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.61/8.81 apply (zenon_L613_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.61/8.81 apply (zenon_L395_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.61/8.81 apply (zenon_L346_); trivial. % 8.61/8.81 apply (zenon_L501_); trivial. % 8.61/8.81 (* end of lemma zenon_L615_ *) % 8.61/8.81 assert (zenon_L616_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> False). % 8.61/8.81 do 0 intro. intros zenon_H2df zenon_Ha3 zenon_H276 zenon_Had zenon_H67 zenon_H3b zenon_H7d zenon_H1d9 zenon_Hf4. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.61/8.81 apply (zenon_L245_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.61/8.81 apply (zenon_L110_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.61/8.81 apply (zenon_L396_); trivial. % 8.61/8.81 apply (zenon_L319_); trivial. % 8.61/8.81 (* end of lemma zenon_L616_ *) % 8.61/8.81 assert (zenon_L617_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 8.61/8.81 do 0 intro. intros zenon_Hc5 zenon_Hc2 zenon_Hf4 zenon_H1d9 zenon_H7d zenon_H67 zenon_H276 zenon_Ha3 zenon_H2df zenon_H3b zenon_H78 zenon_H170 zenon_H14e. % 8.61/8.81 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_H24 | zenon_intro zenon_Hc6 ]. % 8.61/8.81 apply (zenon_L341_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Had | zenon_intro zenon_Hc7 ]. % 8.61/8.81 apply (zenon_L616_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H80 | zenon_intro zenon_Hc3 ]. % 8.61/8.81 apply (zenon_L40_); trivial. % 8.61/8.81 apply (zenon_L111_); trivial. % 8.61/8.81 (* end of lemma zenon_L617_ *) % 8.61/8.81 assert (zenon_L618_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (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))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 8.61/8.81 do 0 intro. intros zenon_H2e8 zenon_H78 zenon_H2df zenon_Ha3 zenon_H67 zenon_H7d zenon_H1d9 zenon_Hf4 zenon_Hc2 zenon_Hc5 zenon_H2d2 zenon_H9a zenon_H29f zenon_H71 zenon_H170 zenon_H14e zenon_H2d4 zenon_Ha8 zenon_H3b zenon_Heb zenon_H5a. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2e8); [ zenon_intro zenon_H276 | zenon_intro zenon_H2e9 ]. % 8.61/8.81 apply (zenon_L617_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2e9); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H2ea ]. % 8.61/8.81 apply (zenon_L564_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_H99 | zenon_intro zenon_H98 ]. % 8.61/8.81 apply (zenon_L346_); trivial. % 8.61/8.81 apply (zenon_L53_); trivial. % 8.61/8.81 (* end of lemma zenon_L618_ *) % 8.61/8.81 assert (zenon_L619_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (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))))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 8.61/8.81 do 0 intro. intros zenon_H1d9 zenon_H73 zenon_Hab zenon_H2e8 zenon_H2df zenon_Ha3 zenon_H67 zenon_Hc2 zenon_Hc5 zenon_H2d2 zenon_H9a zenon_H29f zenon_H170 zenon_H14e zenon_H2d4 zenon_Ha8 zenon_Heb zenon_H5a zenon_H2fc zenon_H1d7 zenon_H3a zenon_H197 zenon_H12b zenon_H124 zenon_H2bf zenon_H1dc zenon_H1dd zenon_H169 zenon_H2c0 zenon_H2b8 zenon_H2b5 zenon_H109 zenon_H22e zenon_H31 zenon_H2b zenon_H129 zenon_H1f6 zenon_H2a5 zenon_H2a4 zenon_H270 zenon_H1d3 zenon_Hb7 zenon_H192 zenon_H145 zenon_H285 zenon_H295 zenon_H2a3 zenon_Hb4 zenon_H25 zenon_H150 zenon_H1f zenon_H2a2 zenon_H2a1 zenon_H282 zenon_H137 zenon_H173 zenon_H27f zenon_H127 zenon_H11f zenon_H16d zenon_Hf9 zenon_Hd0 zenon_H22d zenon_H74 zenon_H6c zenon_H322 zenon_Hbf zenon_H11e zenon_H94 zenon_H2d8 zenon_Hff zenon_H19a zenon_H329 zenon_H303 zenon_H331 zenon_H153 zenon_H10c zenon_H32e zenon_H35e zenon_H35d zenon_Hba zenon_Hf3 zenon_H134 zenon_H300 zenon_H336 zenon_H164 zenon_H2f3 zenon_H2c9 zenon_H36 zenon_Hf8 zenon_H2e2 zenon_He4 zenon_H105 zenon_H34d zenon_H2f8 zenon_H36a zenon_He7 zenon_H78 zenon_H1d zenon_H90 zenon_H3b zenon_H7d. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.61/8.81 apply (zenon_L543_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.61/8.81 apply (zenon_L77_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2e8); [ zenon_intro zenon_H276 | zenon_intro zenon_H2e9 ]. % 8.61/8.81 apply (zenon_L245_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2e9); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H2ea ]. % 8.61/8.81 apply (zenon_L564_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_H99 | zenon_intro zenon_H98 ]. % 8.61/8.81 apply (zenon_L346_); trivial. % 8.61/8.81 apply (zenon_L53_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.61/8.81 apply (zenon_L77_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.61/8.81 apply (zenon_L20_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2e8); [ zenon_intro zenon_H276 | zenon_intro zenon_H2e9 ]. % 8.61/8.81 apply (zenon_L614_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2e9); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H2ea ]. % 8.61/8.81 apply (zenon_L564_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_H99 | zenon_intro zenon_H98 ]. % 8.61/8.81 apply (zenon_L346_); trivial. % 8.61/8.81 apply (zenon_L602_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.61/8.81 apply (zenon_L395_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.61/8.81 apply (zenon_L346_); trivial. % 8.61/8.81 apply (zenon_L501_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.61/8.81 apply (zenon_L93_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.61/8.81 apply (zenon_L396_); trivial. % 8.61/8.81 apply (zenon_L615_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.61/8.81 apply (zenon_L618_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.61/8.81 apply (zenon_L93_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.61/8.81 apply (zenon_L396_); trivial. % 8.61/8.81 apply (zenon_L319_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.61/8.81 apply (zenon_L80_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.61/8.81 apply (zenon_L565_); trivial. % 8.61/8.81 apply (zenon_L81_); trivial. % 8.61/8.81 (* end of lemma zenon_L619_ *) % 8.61/8.81 assert (zenon_L620_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (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 (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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 (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 8.61/8.81 do 0 intro. intros zenon_Heb zenon_H2f8 zenon_H34d zenon_H2e2 zenon_Hf8 zenon_H36 zenon_H2c9 zenon_H2f3 zenon_H164 zenon_H2e8 zenon_H336 zenon_H2df zenon_H9a zenon_H300 zenon_H90 zenon_H134 zenon_Hf3 zenon_Hba zenon_H35d zenon_H35e zenon_H32e zenon_H10c zenon_H2d4 zenon_H2d2 zenon_Hc5 zenon_H153 zenon_H331 zenon_H303 zenon_H329 zenon_H19a zenon_H94 zenon_H11e zenon_Hbf zenon_H322 zenon_H6c zenon_H74 zenon_H170 zenon_H22d zenon_Hf9 zenon_H29f zenon_H16d zenon_H67 zenon_H11f zenon_H127 zenon_H27f zenon_H173 zenon_H137 zenon_H282 zenon_H2a1 zenon_H2a2 zenon_H1f zenon_H150 zenon_H25 zenon_Hb4 zenon_H2a3 zenon_H295 zenon_H285 zenon_H145 zenon_H192 zenon_H78 zenon_Hb7 zenon_H1d3 zenon_H270 zenon_H2a4 zenon_H2a5 zenon_H1f6 zenon_H129 zenon_H7d zenon_H2b zenon_H31 zenon_H22e zenon_H2b5 zenon_H2b8 zenon_H2c0 zenon_H169 zenon_H1dd zenon_H1dc zenon_H2bf zenon_H124 zenon_H1d zenon_Hc2 zenon_H1d9 zenon_Hab zenon_H73 zenon_Ha3 zenon_H12b zenon_H197 zenon_H3a zenon_Ha8 zenon_H1d7 zenon_H2fc zenon_H3b zenon_H143 zenon_H154 zenon_H2d8 zenon_He4 zenon_Hd0 zenon_Hff zenon_Hd1 zenon_H105 zenon_H109 zenon_H5a zenon_He7. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.61/8.81 apply (zenon_L77_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.61/8.81 apply (zenon_L20_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.61/8.81 apply (zenon_L502_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.61/8.81 apply (zenon_L508_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.61/8.81 apply (zenon_L604_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.61/8.81 apply (zenon_L97_); trivial. % 8.61/8.81 apply (zenon_L608_); trivial. % 8.61/8.81 (* end of lemma zenon_L620_ *) % 8.61/8.81 assert (zenon_L621_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (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). % 8.61/8.81 do 0 intro. intros zenon_H2b8 zenon_Ha8 zenon_H7d zenon_H329 zenon_Ha2 zenon_H41 zenon_H2b5 zenon_H197 zenon_H15a zenon_H109 zenon_He7 zenon_H3a zenon_H3b zenon_H105 zenon_Hd4 zenon_Hff zenon_Hd0 zenon_He4 zenon_H12b zenon_H143 zenon_H2d8 zenon_H5a zenon_H16d. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H2b9 ]. % 8.61/8.81 apply (zenon_L505_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_H35 | zenon_intro zenon_H2ba ]. % 8.61/8.81 apply (zenon_L247_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H16b | zenon_intro zenon_He5 ]. % 8.61/8.81 apply (zenon_L472_); trivial. % 8.61/8.81 apply (zenon_L506_); trivial. % 8.61/8.81 (* end of lemma zenon_L621_ *) % 8.61/8.81 assert (zenon_L622_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (op (e0) (e0))) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (op (e0) (e2))) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 8.61/8.81 do 0 intro. intros zenon_H11e zenon_H24 zenon_H12e zenon_H164 zenon_H191 zenon_H118 zenon_Hd6 zenon_H7d. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.61/8.81 apply (zenon_L304_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.61/8.81 apply (zenon_L314_); trivial. % 8.61/8.81 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.61/8.81 apply (zenon_L70_); trivial. % 8.61/8.81 apply (zenon_L81_); trivial. % 8.61/8.81 (* end of lemma zenon_L622_ *) % 8.61/8.81 assert (zenon_L623_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> False). % 8.61/8.81 do 0 intro. intros zenon_Hbf zenon_H78 zenon_H154 zenon_H7d zenon_H2f8 zenon_H24 zenon_H134 zenon_H94 zenon_H2d2 zenon_H1df zenon_H91. % 8.61/8.81 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H7e | zenon_intro zenon_Hc0 ]. % 8.61/8.82 apply (zenon_L128_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H93 | zenon_intro zenon_Hc1 ]. % 8.61/8.82 apply (zenon_L97_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H3b | zenon_intro zenon_Hbd ]. % 8.61/8.82 apply (zenon_L396_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_Had | zenon_intro zenon_H2f9 ]. % 8.61/8.82 apply (zenon_L397_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H29 | zenon_intro zenon_H2fa ]. % 8.61/8.82 apply (zenon_L104_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H93 | zenon_intro zenon_Ha7 ]. % 8.61/8.82 apply (zenon_L320_); trivial. % 8.61/8.82 apply (zenon_L431_); trivial. % 8.61/8.82 (* end of lemma zenon_L623_ *) % 8.61/8.82 assert (zenon_L624_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 8.61/8.82 do 0 intro. intros zenon_H10c zenon_H73 zenon_H2c9 zenon_H191 zenon_H303 zenon_H67 zenon_H143 zenon_H164 zenon_H6b zenon_H1df zenon_H2d2 zenon_H94 zenon_H134 zenon_H24 zenon_H2f8 zenon_H7d zenon_H154 zenon_H78 zenon_Hbf zenon_H105 zenon_Hd1 zenon_Hff zenon_Hd0 zenon_H5a zenon_He4. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.61/8.82 apply (zenon_L508_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.61/8.82 apply (zenon_L509_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.61/8.82 apply (zenon_L97_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.61/8.82 apply (zenon_L261_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.61/8.82 apply (zenon_L534_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.61/8.82 apply (zenon_L623_); trivial. % 8.61/8.82 apply (zenon_L434_); trivial. % 8.61/8.82 (* end of lemma zenon_L624_ *) % 8.61/8.82 assert (zenon_L625_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 8.61/8.82 do 0 intro. intros zenon_H303 zenon_H67 zenon_H143 zenon_H191 zenon_H1df zenon_H2d2 zenon_H94 zenon_H134 zenon_H24 zenon_H2f8 zenon_H7d zenon_H154 zenon_H78 zenon_Hbf zenon_Hff zenon_Hd6. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.61/8.82 apply (zenon_L261_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.61/8.82 apply (zenon_L149_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.61/8.82 apply (zenon_L623_); trivial. % 8.61/8.82 apply (zenon_L107_); trivial. % 8.61/8.82 (* end of lemma zenon_L625_ *) % 8.61/8.82 assert (zenon_L626_ : (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> False). % 8.61/8.82 do 0 intro. intros zenon_H78 zenon_H191 zenon_H165. % 8.61/8.82 cut (((op (e2) (e1)) = (e2)) = ((e0) = (e2))). % 8.61/8.82 intro zenon_D_pnotp. % 8.61/8.82 apply zenon_H78. % 8.61/8.82 rewrite <- zenon_D_pnotp. % 8.61/8.82 exact zenon_H191. % 8.61/8.82 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.61/8.82 cut (((op (e2) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H36d]. % 8.61/8.82 congruence. % 8.61/8.82 exact (zenon_H36d zenon_H165). % 8.61/8.82 apply zenon_H4b. apply refl_equal. % 8.61/8.82 (* end of lemma zenon_L626_ *) % 8.61/8.82 assert (zenon_L627_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 8.61/8.82 do 0 intro. intros zenon_H1d3 zenon_H14e zenon_H1df. % 8.61/8.82 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 8.61/8.82 intro zenon_D_pnotp. % 8.61/8.82 apply zenon_H1d3. % 8.61/8.82 rewrite <- zenon_D_pnotp. % 8.61/8.82 exact zenon_H14e. % 8.61/8.82 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1e0]. % 8.61/8.82 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 8.61/8.82 congruence. % 8.61/8.82 apply zenon_H172. apply refl_equal. % 8.61/8.82 apply zenon_H1e0. apply sym_equal. exact zenon_H1df. % 8.61/8.82 (* end of lemma zenon_L627_ *) % 8.61/8.82 assert (zenon_L628_ : (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 8.61/8.82 do 0 intro. intros zenon_H169 zenon_H191 zenon_H1d8. % 8.61/8.82 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e3) (e1)))). % 8.61/8.82 intro zenon_D_pnotp. % 8.61/8.82 apply zenon_H169. % 8.61/8.82 rewrite <- zenon_D_pnotp. % 8.61/8.82 exact zenon_H191. % 8.61/8.82 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 8.61/8.82 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 8.61/8.82 congruence. % 8.61/8.82 apply zenon_H16a. apply refl_equal. % 8.61/8.82 apply zenon_H1db. apply sym_equal. exact zenon_H1d8. % 8.61/8.82 (* end of lemma zenon_L628_ *) % 8.61/8.82 assert (zenon_L629_ : ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((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))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (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)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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 (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.61/8.82 do 0 intro. intros zenon_H14e zenon_H6b zenon_H191 zenon_H2f8 zenon_H34d zenon_H105 zenon_He4 zenon_H2bf zenon_H2e2 zenon_Hf8 zenon_H2a3 zenon_H36 zenon_H124 zenon_H11f zenon_Hf9 zenon_H285 zenon_H27f zenon_H282 zenon_H150 zenon_Hb7 zenon_H2c9 zenon_H295 zenon_H1dc zenon_H2c0 zenon_H270 zenon_H1f zenon_H16d zenon_H2f3 zenon_H164 zenon_H2fc zenon_H3a zenon_H73 zenon_Hb4 zenon_H2e8 zenon_H2a4 zenon_H1dd zenon_H336 zenon_H2a1 zenon_H137 zenon_H2df zenon_H9a zenon_H300 zenon_H90 zenon_H134 zenon_Hf3 zenon_Hba zenon_H35d zenon_H35e zenon_H6c zenon_H12b zenon_H129 zenon_H2a5 zenon_H32e zenon_H10c zenon_H145 zenon_H2d4 zenon_H2d2 zenon_H29f zenon_Hc5 zenon_H170 zenon_H153 zenon_H22e zenon_H25 zenon_Hab zenon_H2b zenon_H22d zenon_H127 zenon_H173 zenon_H331 zenon_Hd0 zenon_H2b5 zenon_H1d3 zenon_Hc2 zenon_H303 zenon_H329 zenon_H78 zenon_H7d zenon_H19a zenon_H192 zenon_H109 zenon_He7 zenon_Hff zenon_H2d8 zenon_H169 zenon_H31 zenon_H2a2 zenon_H74 zenon_H197 zenon_H67 zenon_H2b8 zenon_Ha3 zenon_H1f6 zenon_Ha8 zenon_H1d7 zenon_H1d9. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H1df | zenon_intro zenon_H1de ]. % 8.61/8.82 apply (zenon_L627_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H1e1 ]. % 8.61/8.82 apply (zenon_L313_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H1b1 ]. % 8.61/8.82 apply (zenon_L628_); trivial. % 8.61/8.82 apply (zenon_L593_); trivial. % 8.61/8.82 (* end of lemma zenon_L629_ *) % 8.61/8.82 assert (zenon_L630_ : (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> False). % 8.61/8.82 do 0 intro. intros zenon_H129 zenon_H93 zenon_H108. % 8.61/8.82 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (e2)) = (op (e1) (e3)))). % 8.61/8.82 intro zenon_D_pnotp. % 8.61/8.82 apply zenon_H129. % 8.61/8.82 rewrite <- zenon_D_pnotp. % 8.61/8.82 exact zenon_H93. % 8.61/8.82 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10b]. % 8.61/8.82 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 8.61/8.82 congruence. % 8.61/8.82 apply zenon_H2d. apply refl_equal. % 8.61/8.82 apply zenon_H10b. apply sym_equal. exact zenon_H108. % 8.61/8.82 (* end of lemma zenon_L630_ *) % 8.61/8.82 assert (zenon_L631_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.61/8.82 do 0 intro. intros zenon_H2b5 zenon_H30 zenon_Hd0 zenon_H16b zenon_H93 zenon_H129 zenon_H109 zenon_H195. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H2b6 ]. % 8.61/8.82 apply (zenon_L47_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H35 | zenon_intro zenon_H2b7 ]. % 8.61/8.82 apply (zenon_L106_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H108 | zenon_intro zenon_Hb3 ]. % 8.61/8.82 apply (zenon_L630_); trivial. % 8.61/8.82 apply (zenon_L473_); trivial. % 8.61/8.82 (* end of lemma zenon_L631_ *) % 8.61/8.82 assert (zenon_L632_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.61/8.82 do 0 intro. intros zenon_H2b8 zenon_H67 zenon_Hb4 zenon_H73 zenon_H2b5 zenon_H30 zenon_Hd0 zenon_H16d zenon_H93 zenon_H129 zenon_H109 zenon_H195. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H2b9 ]. % 8.61/8.82 apply (zenon_L343_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_H35 | zenon_intro zenon_H2ba ]. % 8.61/8.82 apply (zenon_L119_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H16b | zenon_intro zenon_He5 ]. % 8.61/8.82 apply (zenon_L631_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H2b6 ]. % 8.61/8.82 apply (zenon_L47_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H35 | zenon_intro zenon_H2b7 ]. % 8.61/8.82 apply (zenon_L267_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H108 | zenon_intro zenon_Hb3 ]. % 8.61/8.82 apply (zenon_L630_); trivial. % 8.61/8.82 apply (zenon_L473_); trivial. % 8.61/8.82 (* end of lemma zenon_L632_ *) % 8.61/8.82 assert (zenon_L633_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((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))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (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)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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 (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.61/8.82 do 0 intro. intros zenon_H1bd zenon_H191 zenon_H2f8 zenon_H34d zenon_H105 zenon_He4 zenon_H2bf zenon_H2e2 zenon_Hf8 zenon_H2a3 zenon_H36 zenon_H124 zenon_H11f zenon_Hf9 zenon_H285 zenon_H27f zenon_H282 zenon_H150 zenon_Hb7 zenon_H2c9 zenon_H295 zenon_H1dc zenon_H2c0 zenon_H270 zenon_H1f zenon_H16d zenon_H2f3 zenon_H164 zenon_H2fc zenon_H3a zenon_Hb4 zenon_H2e8 zenon_H2a4 zenon_H1dd zenon_H336 zenon_H2a1 zenon_H137 zenon_H2df zenon_H9a zenon_H300 zenon_H90 zenon_H134 zenon_Hf3 zenon_Hba zenon_H35d zenon_H35e zenon_H6c zenon_H12b zenon_H129 zenon_H2a5 zenon_H32e zenon_H10c zenon_H145 zenon_H2d4 zenon_H2d2 zenon_H29f zenon_Hc5 zenon_H170 zenon_H153 zenon_H22e zenon_H25 zenon_Hab zenon_H2b zenon_H22d zenon_H127 zenon_H173 zenon_H331 zenon_Hd0 zenon_H2b5 zenon_H1d3 zenon_Hc2 zenon_H303 zenon_H329 zenon_H78 zenon_H7d zenon_H19a zenon_H192 zenon_H109 zenon_He7 zenon_Hff zenon_H2d8 zenon_H169 zenon_H31 zenon_H2a2 zenon_H74 zenon_H197 zenon_H67 zenon_H2b8 zenon_Ha3 zenon_H1f6 zenon_Ha8 zenon_H1d7 zenon_H1d9. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H1bd). zenon_intro zenon_H73. zenon_intro zenon_H1be. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_H6b. zenon_intro zenon_H180. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H14e. zenon_intro zenon_H30. % 8.61/8.82 apply (zenon_L629_); trivial. % 8.61/8.82 (* end of lemma zenon_L633_ *) % 8.61/8.82 assert (zenon_L634_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> False). % 8.61/8.82 do 0 intro. intros zenon_H221 zenon_H1f6 zenon_H191. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H221). zenon_intro zenon_H98. zenon_intro zenon_H222. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H222). zenon_intro zenon_H195. zenon_intro zenon_H1a5. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H1a5). zenon_intro zenon_H3b. zenon_intro zenon_H3b. % 8.61/8.82 apply (zenon_L198_); trivial. % 8.61/8.82 (* end of lemma zenon_L634_ *) % 8.61/8.82 assert (zenon_L635_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 8.61/8.82 do 0 intro. intros zenon_H21d zenon_H191 zenon_H192. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H98. zenon_intro zenon_H21e. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H21e). zenon_intro zenon_H195. zenon_intro zenon_H19f. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H19f). zenon_intro zenon_H7e. zenon_intro zenon_Hc8. % 8.61/8.82 apply (zenon_L125_); trivial. % 8.61/8.82 (* end of lemma zenon_L635_ *) % 8.61/8.82 assert (zenon_L636_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.61/8.82 do 0 intro. intros zenon_H329 zenon_H78 zenon_H30 zenon_H93 zenon_H129 zenon_H191 zenon_H197 zenon_H59 zenon_H98. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hfe | zenon_intro zenon_H32a ]. % 8.61/8.82 apply (zenon_L394_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H108 | zenon_intro zenon_H32b ]. % 8.61/8.82 apply (zenon_L630_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H3c | zenon_intro zenon_He8 ]. % 8.61/8.82 apply (zenon_L191_); trivial. % 8.61/8.82 apply (zenon_L492_); trivial. % 8.61/8.82 (* end of lemma zenon_L636_ *) % 8.61/8.82 assert (zenon_L637_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = 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(e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.61/8.82 do 0 intro. intros zenon_H2fc zenon_H1d7 zenon_Ha8 zenon_H1f6 zenon_H329 zenon_H78 zenon_H129 zenon_H192 zenon_Ha3 zenon_Hab zenon_H1d9 zenon_Hc2 zenon_H7d zenon_H74 zenon_H6c zenon_H153 zenon_H67 zenon_H31 zenon_H25 zenon_H22e zenon_H322 zenon_Hbf zenon_H11e zenon_H94 zenon_H2b8 zenon_H2a2 zenon_H169 zenon_H2d8 zenon_Hff zenon_He7 zenon_H109 zenon_H19a zenon_H303 zenon_H1d3 zenon_H2b5 zenon_Hd0 zenon_H331 zenon_H173 zenon_H127 zenon_H22d zenon_H2b zenon_H170 zenon_Hc5 zenon_H29f zenon_H2d2 zenon_H2d4 zenon_H145 zenon_H10c zenon_H32e zenon_H2a5 zenon_H12b zenon_H35e zenon_H35d zenon_Hba zenon_Hf3 zenon_H134 zenon_H90 zenon_H300 zenon_H9a zenon_H2df zenon_H137 zenon_H2a1 zenon_H336 zenon_H1dd zenon_H2a4 zenon_H2e8 zenon_H3a zenon_H164 zenon_H2f3 zenon_H16d zenon_H1f zenon_H270 zenon_H2c0 zenon_H1dc zenon_H295 zenon_H2c9 zenon_Hb7 zenon_H150 zenon_H282 zenon_H27f zenon_H285 zenon_Hf9 zenon_H11f zenon_H124 zenon_H36 zenon_H2a3 zenon_Hf8 zenon_H2e2 zenon_H2bf zenon_He4 zenon_H105 zenon_H34d zenon_H2f8 zenon_Hb4 zenon_H73 zenon_H191 zenon_H197 zenon_Heb zenon_H98. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H118. zenon_intro zenon_H18a. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.61/8.82 apply (zenon_L193_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.61/8.82 apply (zenon_L194_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.61/8.82 apply (zenon_L195_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.61/8.82 apply (zenon_L117_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.61/8.82 apply (zenon_L514_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.61/8.82 apply (zenon_L515_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.61/8.82 apply (zenon_L460_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.61/8.82 apply (zenon_L517_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.61/8.82 apply (zenon_L197_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H1a0). zenon_intro zenon_H24. zenon_intro zenon_H1a1. % 8.61/8.82 apply (zenon_L303_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.61/8.82 apply (zenon_L578_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.61/8.82 apply (zenon_L200_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.61/8.82 apply (zenon_L135_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.61/8.82 apply (zenon_L519_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_H30. zenon_intro zenon_H1b3. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H1b3). zenon_intro zenon_H14e. zenon_intro zenon_H1d6. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H195. zenon_intro zenon_H98. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.61/8.82 apply (zenon_L543_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.61/8.82 apply (zenon_L527_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.61/8.82 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H7e | zenon_intro zenon_Hc0 ]. % 8.61/8.82 apply (zenon_L23_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H93 | zenon_intro zenon_Hc1 ]. % 8.61/8.82 apply (zenon_L632_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H3b | zenon_intro zenon_Hbd ]. % 8.61/8.82 apply (zenon_L198_); trivial. % 8.61/8.82 apply (zenon_L38_); trivial. % 8.61/8.82 apply (zenon_L343_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.61/8.82 apply (zenon_L138_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.61/8.82 apply (zenon_L579_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.61/8.82 apply (zenon_L520_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.61/8.82 apply (zenon_L580_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.61/8.82 apply (zenon_L633_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.61/8.82 apply (zenon_L522_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.61/8.82 apply (zenon_L523_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.61/8.82 apply (zenon_L146_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.61/8.82 apply (zenon_L524_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.61/8.82 apply (zenon_L148_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.61/8.82 apply (zenon_L151_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.61/8.82 apply (zenon_L206_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.61/8.82 apply (zenon_L525_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.61/8.82 apply (zenon_L355_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.61/8.82 apply (zenon_L356_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.61/8.82 apply (zenon_L526_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.61/8.82 apply (zenon_L357_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.61/8.82 apply (zenon_L464_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.61/8.82 apply (zenon_L465_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.61/8.82 apply (zenon_L188_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.61/8.82 apply (zenon_L361_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.61/8.82 apply (zenon_L528_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.61/8.82 apply (zenon_L529_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.61/8.82 apply (zenon_L364_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.61/8.82 apply (zenon_L530_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.61/8.82 apply (zenon_L241_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.61/8.82 apply (zenon_L242_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.61/8.82 apply (zenon_L217_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.61/8.82 apply (zenon_L272_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.61/8.82 apply (zenon_L273_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.61/8.82 apply (zenon_L594_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.61/8.82 apply (zenon_L369_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.61/8.82 apply (zenon_L370_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.61/8.82 apply (zenon_L223_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.61/8.82 apply (zenon_L275_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.61/8.82 apply (zenon_L537_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.61/8.82 apply (zenon_L373_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.61/8.82 apply (zenon_L538_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.61/8.82 apply (zenon_L539_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.61/8.82 apply (zenon_L540_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.61/8.82 apply (zenon_L378_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.61/8.82 apply (zenon_L379_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H21f). zenon_intro zenon_H98. zenon_intro zenon_H220. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H220). zenon_intro zenon_H195. zenon_intro zenon_H1a2. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H1a2). zenon_intro zenon_H93. zenon_intro zenon_H191. % 8.61/8.82 apply (zenon_L632_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.61/8.82 apply (zenon_L634_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.61/8.82 apply (zenon_L382_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.61/8.82 apply (zenon_L383_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.61/8.82 apply (zenon_L386_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.61/8.82 apply (zenon_L387_); trivial. % 8.61/8.82 apply (zenon_L388_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H41. zenon_intro zenon_H4a. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H4a). zenon_intro zenon_H154. zenon_intro zenon_H2c3. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.61/8.82 apply (zenon_L193_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.61/8.82 apply (zenon_L194_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.61/8.82 apply (zenon_L116_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.61/8.82 apply (zenon_L118_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.61/8.82 apply (zenon_L514_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.61/8.82 apply (zenon_L515_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.61/8.82 apply (zenon_L277_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.61/8.82 apply (zenon_L389_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.61/8.82 apply (zenon_L129_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.61/8.82 apply (zenon_L278_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.61/8.82 apply (zenon_L199_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.61/8.82 apply (zenon_L200_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.61/8.82 apply (zenon_L202_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.61/8.82 apply (zenon_L546_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_H30. zenon_intro zenon_H1b3. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H1b3). zenon_intro zenon_H14e. zenon_intro zenon_H1d6. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.61/8.82 apply (zenon_L73_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.61/8.82 apply (zenon_L572_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.61/8.82 apply (zenon_L626_); trivial. % 8.61/8.82 apply (zenon_L627_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.61/8.82 apply (zenon_L138_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.61/8.82 apply (zenon_L579_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.61/8.82 apply (zenon_L520_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.61/8.82 apply (zenon_L580_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.61/8.82 apply (zenon_L633_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.61/8.82 apply (zenon_L522_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.61/8.82 apply (zenon_L523_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.61/8.82 apply (zenon_L203_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.61/8.82 apply (zenon_L524_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.61/8.82 apply (zenon_L204_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.61/8.82 apply (zenon_L150_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.61/8.82 apply (zenon_L206_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.61/8.82 apply (zenon_L207_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.61/8.82 apply (zenon_L208_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.61/8.82 apply (zenon_L356_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.61/8.82 apply (zenon_L526_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.61/8.82 apply (zenon_L357_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.61/8.82 apply (zenon_L209_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.61/8.82 apply (zenon_L210_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.61/8.82 apply (zenon_L211_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.61/8.82 apply (zenon_L598_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.61/8.82 apply (zenon_L547_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.61/8.82 apply (zenon_L529_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.61/8.82 apply (zenon_L213_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.61/8.82 apply (zenon_L279_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.61/8.82 apply (zenon_L215_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.61/8.82 apply (zenon_L216_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.61/8.82 apply (zenon_L217_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.61/8.82 apply (zenon_L218_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.61/8.82 apply (zenon_L219_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.61/8.82 apply (zenon_L548_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.61/8.82 apply (zenon_L369_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.61/8.82 apply (zenon_L370_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.61/8.82 apply (zenon_L223_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.61/8.82 apply (zenon_L281_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.61/8.82 apply (zenon_L225_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.61/8.82 apply (zenon_L372_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.61/8.82 apply (zenon_L549_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.61/8.82 apply (zenon_L376_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.61/8.82 apply (zenon_L540_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.61/8.82 apply (zenon_L378_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.61/8.82 apply (zenon_L635_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.61/8.82 apply (zenon_L597_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.61/8.82 apply (zenon_L634_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.61/8.82 apply (zenon_L382_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.61/8.82 apply (zenon_L383_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.61/8.82 apply (zenon_L386_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.61/8.82 apply (zenon_L387_); trivial. % 8.61/8.82 apply (zenon_L388_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H4c. zenon_intro zenon_H57. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.61/8.82 apply (zenon_L193_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.61/8.82 apply (zenon_L194_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.61/8.82 apply (zenon_L282_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.61/8.82 apply (zenon_L117_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.61/8.82 apply (zenon_L514_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.61/8.82 apply (zenon_L515_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.61/8.82 apply (zenon_L283_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.61/8.82 apply (zenon_L517_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.61/8.82 apply (zenon_L197_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.61/8.82 apply (zenon_L284_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.61/8.82 apply (zenon_L578_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.61/8.82 apply (zenon_L285_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.61/8.82 apply (zenon_L135_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.61/8.82 apply (zenon_L519_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.61/8.82 apply (zenon_L410_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.61/8.82 apply (zenon_L138_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.61/8.82 apply (zenon_L579_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.61/8.82 apply (zenon_L520_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.61/8.82 apply (zenon_L286_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.61/8.82 apply (zenon_L633_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.61/8.82 apply (zenon_L522_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.61/8.82 apply (zenon_L523_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.61/8.82 apply (zenon_L146_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.61/8.82 apply (zenon_L524_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.61/8.82 apply (zenon_L411_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.61/8.82 apply (zenon_L151_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.61/8.82 apply (zenon_L206_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.61/8.82 apply (zenon_L287_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.61/8.82 apply (zenon_L355_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.61/8.82 apply (zenon_L356_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.61/8.82 apply (zenon_L412_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.61/8.82 apply (zenon_L357_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.61/8.82 apply (zenon_L464_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.61/8.82 apply (zenon_L465_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.61/8.82 apply (zenon_L188_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.61/8.82 apply (zenon_L598_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H1f2). zenon_intro zenon_H191. zenon_intro zenon_H1f3. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H93. zenon_intro zenon_H183. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H183). zenon_intro zenon_H6b. zenon_intro zenon_H73. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.61/8.82 apply (zenon_L4_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.61/8.82 apply (zenon_L499_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.61/8.82 apply (zenon_L100_); trivial. % 8.61/8.82 apply (zenon_L629_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.61/8.82 apply (zenon_L529_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.61/8.82 apply (zenon_L364_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.61/8.82 apply (zenon_L530_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.61/8.82 apply (zenon_L241_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.61/8.82 apply (zenon_L242_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.61/8.82 apply (zenon_L217_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.61/8.82 apply (zenon_L272_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.61/8.82 apply (zenon_L407_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.61/8.82 apply (zenon_L594_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.61/8.82 apply (zenon_L369_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.61/8.82 apply (zenon_L370_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.61/8.82 apply (zenon_L223_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.61/8.82 apply (zenon_L224_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.61/8.82 apply (zenon_L293_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.61/8.82 apply (zenon_L373_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.61/8.82 apply (zenon_L600_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.61/8.82 apply (zenon_L539_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.61/8.82 apply (zenon_L414_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.61/8.82 apply (zenon_L378_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.61/8.82 apply (zenon_L415_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.61/8.82 apply (zenon_L601_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.61/8.82 apply (zenon_L634_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.61/8.82 apply (zenon_L382_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.61/8.82 apply (zenon_L383_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.61/8.82 apply (zenon_L386_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.61/8.82 apply (zenon_L387_); trivial. % 8.61/8.82 apply (zenon_L388_); trivial. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H59. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.61/8.82 apply (zenon_L193_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.61/8.82 apply (zenon_L194_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.61/8.82 apply (zenon_L116_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.61/8.82 apply (zenon_L417_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.61/8.82 apply (zenon_L514_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.61/8.82 apply (zenon_L515_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.61/8.82 apply (zenon_L516_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.61/8.82 apply (zenon_L333_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.61/8.82 apply (zenon_L129_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H1a0). zenon_intro zenon_H24. zenon_intro zenon_H1a1. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H1a1). zenon_intro zenon_H143. zenon_intro zenon_H1a2. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H1a2). zenon_intro zenon_H93. zenon_intro zenon_H191. % 8.61/8.82 apply (zenon_L636_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.61/8.82 apply (zenon_L199_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.61/8.82 apply (zenon_L296_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.61/8.82 apply (zenon_L202_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.61/8.82 apply (zenon_L459_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.61/8.82 apply (zenon_L418_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.61/8.82 apply (zenon_L138_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.61/8.82 apply (zenon_L579_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.61/8.82 apply (zenon_L520_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.61/8.82 apply (zenon_L580_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.61/8.82 apply (zenon_L419_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.61/8.82 apply (zenon_L522_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.61/8.82 apply (zenon_L523_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.61/8.82 apply (zenon_L203_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.61/8.82 apply (zenon_L334_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.61/8.82 apply (zenon_L204_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.61/8.82 apply (zenon_L150_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.61/8.82 apply (zenon_L206_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.61/8.82 apply (zenon_L297_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.61/8.82 apply (zenon_L298_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.61/8.82 apply (zenon_L356_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.61/8.82 apply (zenon_L421_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.61/8.82 apply (zenon_L357_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.61/8.82 apply (zenon_L209_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.61/8.82 apply (zenon_L210_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.61/8.82 apply (zenon_L211_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.61/8.82 apply (zenon_L422_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H1f2). zenon_intro zenon_H191. zenon_intro zenon_H1f3. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H93. zenon_intro zenon_H183. % 8.61/8.82 apply (zenon_L636_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.61/8.82 apply (zenon_L529_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.61/8.82 apply (zenon_L213_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.61/8.82 apply (zenon_L335_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.61/8.82 apply (zenon_L215_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.61/8.82 apply (zenon_L216_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.61/8.82 apply (zenon_L217_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.61/8.82 apply (zenon_L299_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.61/8.82 apply (zenon_L300_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.61/8.82 apply (zenon_L423_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.61/8.82 apply (zenon_L369_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.61/8.82 apply (zenon_L370_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.61/8.82 apply (zenon_L223_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.61/8.82 apply (zenon_L224_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.61/8.82 apply (zenon_L225_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.61/8.82 apply (zenon_L372_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.61/8.82 apply (zenon_L600_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.61/8.82 apply (zenon_L376_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.61/8.82 apply (zenon_L540_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.61/8.82 apply (zenon_L378_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.61/8.82 apply (zenon_L635_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H21f). zenon_intro zenon_H98. zenon_intro zenon_H220. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H220). zenon_intro zenon_H195. zenon_intro zenon_H1a2. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H1a2). zenon_intro zenon_H93. zenon_intro zenon_H191. % 8.61/8.82 apply (zenon_L636_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.61/8.82 apply (zenon_L634_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.61/8.82 apply (zenon_L382_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.61/8.82 apply (zenon_L383_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.61/8.82 apply (zenon_L386_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.61/8.82 apply (zenon_L387_); trivial. % 8.61/8.82 apply (zenon_L388_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.61/8.82 apply (zenon_L119_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.61/8.82 apply (zenon_L191_); trivial. % 8.61/8.82 apply (zenon_L53_); trivial. % 8.61/8.82 (* end of lemma zenon_L637_ *) % 8.61/8.82 assert (zenon_L638_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (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)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e1)) = (op (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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 8.61/8.82 do 0 intro. intros zenon_H2fc zenon_H1d7 zenon_Ha8 zenon_H1f6 zenon_H329 zenon_H78 zenon_H129 zenon_H192 zenon_Ha3 zenon_Hab zenon_H1d9 zenon_Hc2 zenon_H7d zenon_H74 zenon_H6c zenon_H153 zenon_H67 zenon_H31 zenon_H25 zenon_H22e zenon_H322 zenon_Hbf zenon_H11e zenon_H94 zenon_H2b8 zenon_H2a2 zenon_H169 zenon_H2d8 zenon_Hff zenon_He7 zenon_H109 zenon_H19a zenon_H303 zenon_H1d3 zenon_H2b5 zenon_Hd0 zenon_H331 zenon_H173 zenon_H127 zenon_H22d zenon_H2b zenon_H170 zenon_Hc5 zenon_H29f zenon_H2d2 zenon_H2d4 zenon_H145 zenon_H10c zenon_H32e zenon_H2a5 zenon_H12b zenon_H35e zenon_H35d zenon_Hba zenon_Hf3 zenon_H134 zenon_H90 zenon_H300 zenon_H9a zenon_H2df zenon_H137 zenon_H2a1 zenon_H336 zenon_H1dd zenon_H2a4 zenon_H2e8 zenon_H3a zenon_H164 zenon_H2f3 zenon_H16d zenon_H1f zenon_H270 zenon_H2c0 zenon_H1dc zenon_H295 zenon_H2c9 zenon_Hb7 zenon_H150 zenon_H282 zenon_H27f zenon_H285 zenon_Hf9 zenon_H11f zenon_H124 zenon_H36 zenon_H2a3 zenon_Hf8 zenon_H2e2 zenon_H2bf zenon_He4 zenon_H105 zenon_H34d zenon_H2f8 zenon_Hb4 zenon_H73 zenon_H191 zenon_H197 zenon_Heb. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c1 ]. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.61/8.82 apply (zenon_L303_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.61/8.82 apply (zenon_L119_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.61/8.82 apply (zenon_L191_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H118. zenon_intro zenon_H18a. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.61/8.82 apply (zenon_L543_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.61/8.82 apply (zenon_L527_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.61/8.82 apply (zenon_L22_); trivial. % 8.61/8.82 apply (zenon_L622_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H41. zenon_intro zenon_H4a. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H4a). zenon_intro zenon_H154. zenon_intro zenon_H2c3. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.61/8.82 apply (zenon_L2_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.61/8.82 apply (zenon_L499_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.61/8.82 apply (zenon_L543_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H35d); [ zenon_intro zenon_Hac | zenon_intro zenon_H35f ]. % 8.61/8.82 apply (zenon_L499_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_H358 | zenon_intro zenon_H360 ]. % 8.61/8.82 apply (zenon_L572_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Had | zenon_intro zenon_Hd1 ]. % 8.61/8.82 apply (zenon_L397_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.61/8.82 apply (zenon_L77_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.61/8.82 apply (zenon_L572_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.61/8.82 apply (zenon_L249_); trivial. % 8.61/8.82 apply (zenon_L624_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.61/8.82 apply (zenon_L22_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.61/8.82 apply (zenon_L72_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.61/8.82 apply (zenon_L572_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.61/8.82 apply (zenon_L249_); trivial. % 8.61/8.82 apply (zenon_L625_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.61/8.82 apply (zenon_L72_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.61/8.82 apply (zenon_L572_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.61/8.82 apply (zenon_L626_); trivial. % 8.61/8.82 apply (zenon_L627_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H4c. zenon_intro zenon_H57. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.61/8.82 apply (zenon_L2_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.61/8.82 apply (zenon_L499_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.61/8.82 apply (zenon_L100_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.61/8.82 apply (zenon_L543_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.61/8.82 apply (zenon_L629_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.61/8.82 apply (zenon_L22_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.61/8.82 apply (zenon_L550_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.61/8.82 apply (zenon_L20_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.61/8.82 apply (zenon_L99_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.61/8.82 apply (zenon_L22_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.61/8.82 apply (zenon_L93_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.61/8.82 apply (zenon_L329_); trivial. % 8.61/8.82 apply (zenon_L319_); trivial. % 8.61/8.82 apply (zenon_L16_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H29 | zenon_intro zenon_H2c2 ]. % 8.61/8.82 apply (zenon_L93_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2c2); [ zenon_intro zenon_H3b | zenon_intro zenon_H98 ]. % 8.61/8.82 apply (zenon_L198_); trivial. % 8.61/8.82 apply (zenon_L637_); trivial. % 8.61/8.82 (* end of lemma zenon_L638_ *) % 8.61/8.82 assert (zenon_L639_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((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))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (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)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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 (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.61/8.82 do 0 intro. intros zenon_H36a zenon_Heb zenon_H94 zenon_H11e zenon_Hbf zenon_H322 zenon_H2f8 zenon_H34d zenon_H105 zenon_He4 zenon_H2bf zenon_H2e2 zenon_Hf8 zenon_H2a3 zenon_H36 zenon_H124 zenon_H11f zenon_Hf9 zenon_H285 zenon_H27f zenon_H282 zenon_H150 zenon_Hb7 zenon_H2c9 zenon_H295 zenon_H1dc zenon_H2c0 zenon_H270 zenon_H1f zenon_H16d zenon_H2f3 zenon_H164 zenon_H2fc zenon_H3a zenon_H73 zenon_Hb4 zenon_H2e8 zenon_H2a4 zenon_H1dd zenon_H336 zenon_H2a1 zenon_H137 zenon_H2df zenon_H9a zenon_H300 zenon_H90 zenon_H134 zenon_Hf3 zenon_Hba zenon_H35d zenon_H35e zenon_H6c zenon_H12b zenon_H129 zenon_H2a5 zenon_H32e zenon_H10c zenon_H145 zenon_H2d4 zenon_H2d2 zenon_H29f zenon_Hc5 zenon_H170 zenon_H153 zenon_H22e zenon_H25 zenon_Hab zenon_H2b zenon_H22d zenon_H127 zenon_H173 zenon_H331 zenon_Hd0 zenon_H2b5 zenon_H1d3 zenon_Hc2 zenon_H303 zenon_H329 zenon_H78 zenon_H7d zenon_H19a zenon_H192 zenon_H109 zenon_He7 zenon_Hff zenon_H2d8 zenon_H169 zenon_H31 zenon_H2a2 zenon_H74 zenon_H197 zenon_H67 zenon_H2b8 zenon_Ha3 zenon_H1f6 zenon_Ha8 zenon_H1d7 zenon_H1d9. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H1d | zenon_intro zenon_H2f4 ]. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c1 ]. % 8.61/8.82 apply (zenon_L72_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H29 | zenon_intro zenon_H2c2 ]. % 8.61/8.82 apply (zenon_L93_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2c2); [ zenon_intro zenon_H3b | zenon_intro zenon_H98 ]. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.61/8.82 apply (zenon_L73_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.61/8.82 apply (zenon_L119_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.61/8.82 apply (zenon_L6_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.61/8.82 apply (zenon_L1_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.61/8.82 apply (zenon_L499_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.61/8.82 apply (zenon_L76_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.61/8.82 apply (zenon_L77_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2a4); [ zenon_intro zenon_H26f | zenon_intro zenon_H2ad ]. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.61/8.82 apply (zenon_L77_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.61/8.82 apply (zenon_L20_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.61/8.82 apply (zenon_L461_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.61/8.82 apply (zenon_L502_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.61/8.82 apply (zenon_L253_); trivial. % 8.61/8.82 apply (zenon_L507_); trivial. % 8.61/8.82 apply (zenon_L607_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H274 | zenon_intro zenon_H2ae ]. % 8.61/8.82 apply (zenon_L244_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H276 | zenon_intro zenon_H103 ]. % 8.61/8.82 apply (zenon_L245_); trivial. % 8.61/8.82 apply (zenon_L89_); trivial. % 8.61/8.82 apply (zenon_L610_); trivial. % 8.61/8.82 apply (zenon_L619_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H41. zenon_intro zenon_H4a. % 8.61/8.82 apply (zenon_and_s _ _ zenon_H4a). zenon_intro zenon_H154. zenon_intro zenon_H2c3. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2a2); [ zenon_intro zenon_H1e | zenon_intro zenon_H2b0 ]. % 8.61/8.82 apply (zenon_L1_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b1 ]. % 8.61/8.82 apply (zenon_L82_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H143 | zenon_intro zenon_H14e ]. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.61/8.82 apply (zenon_L77_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.61/8.82 apply (zenon_L20_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2a3); [ zenon_intro zenon_H274 | zenon_intro zenon_H2b2 ]. % 8.61/8.82 apply (zenon_L244_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H2b3 ]. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.61/8.82 apply (zenon_L73_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.61/8.82 apply (zenon_L620_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.61/8.82 apply (zenon_L253_); trivial. % 8.61/8.82 apply (zenon_L621_); trivial. % 8.61/8.82 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H196 | zenon_intro zenon_H1b1 ]. % 8.61/8.83 apply (zenon_L395_); trivial. % 8.61/8.83 apply (zenon_L384_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.61/8.83 apply (zenon_L508_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.61/8.83 apply (zenon_L604_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.61/8.83 apply (zenon_L97_); trivial. % 8.61/8.83 apply (zenon_L606_); trivial. % 8.61/8.83 apply (zenon_L619_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.61/8.83 apply (zenon_L13_); trivial. % 8.61/8.83 apply (zenon_L16_); trivial. % 8.61/8.83 apply (zenon_L602_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H2f4); [ zenon_intro zenon_H2a | zenon_intro zenon_H2f5 ]. % 8.61/8.83 apply (zenon_L20_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1b1 ]. % 8.61/8.83 apply (zenon_L638_); trivial. % 8.61/8.83 apply (zenon_L593_); trivial. % 8.61/8.83 (* end of lemma zenon_L639_ *) % 8.61/8.83 assert (zenon_L640_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.61/8.83 do 0 intro. intros zenon_Hbf zenon_H7d zenon_Hb4 zenon_Hab zenon_H2a zenon_H74 zenon_Had zenon_Hb7 zenon_Ha3 zenon_H9f zenon_H71 zenon_H90 zenon_H94 zenon_H9a zenon_Hba zenon_H4c zenon_Ha8 zenon_H98. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H7e | zenon_intro zenon_Hc0 ]. % 8.61/8.83 apply (zenon_L23_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H93 | zenon_intro zenon_Hc1 ]. % 8.61/8.83 apply (zenon_L37_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H3b | zenon_intro zenon_Hbd ]. % 8.61/8.83 apply (zenon_L12_); trivial. % 8.61/8.83 apply (zenon_L38_); trivial. % 8.61/8.83 (* end of lemma zenon_L640_ *) % 8.61/8.83 assert (zenon_L641_ : (((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 (e2) (op (e2) (e2))) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.61/8.83 do 0 intro. intros zenon_Hc5 zenon_H25 zenon_H1e zenon_H4c zenon_Hba zenon_H9a zenon_H94 zenon_H90 zenon_H9f zenon_Ha3 zenon_Hb7 zenon_H74 zenon_H2a zenon_Hb4 zenon_Ha8 zenon_H78 zenon_Hb0 zenon_Hab zenon_H7d zenon_H71 zenon_Hbf zenon_Hc2 zenon_H98. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_H24 | zenon_intro zenon_Hc6 ]. % 8.61/8.83 apply (zenon_L2_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Had | zenon_intro zenon_Hc7 ]. % 8.61/8.83 apply (zenon_L640_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H80 | zenon_intro zenon_Hc3 ]. % 8.61/8.83 apply (zenon_L41_); trivial. % 8.61/8.83 apply (zenon_L42_); trivial. % 8.61/8.83 (* end of lemma zenon_L641_ *) % 8.61/8.83 assert (zenon_L642_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 8.61/8.83 do 0 intro. intros zenon_H10c zenon_Hc2 zenon_Hbf zenon_Hab zenon_Hb4 zenon_H74 zenon_Hb7 zenon_H4c zenon_H25 zenon_Hc5 zenon_Hcb zenon_H6c zenon_Hd0 zenon_Hff zenon_Hf8 zenon_H78 zenon_H1e zenon_Heb zenon_He7 zenon_Hed zenon_Hc9 zenon_Hf9 zenon_H7d zenon_H2a zenon_Hf3 zenon_H98 zenon_Ha3 zenon_He4 zenon_Hd1 zenon_H105 zenon_Ha8 zenon_H9f zenon_H71 zenon_H90 zenon_H94 zenon_H9a zenon_Hba zenon_H3c zenon_H109. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.61/8.83 apply (zenon_L641_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.61/8.83 apply (zenon_L45_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.61/8.83 apply (zenon_L62_); trivial. % 8.61/8.83 apply (zenon_L63_); trivial. % 8.61/8.83 (* end of lemma zenon_L642_ *) % 8.61/8.83 assert (zenon_L643_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((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)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (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) (op (e2) (e2))) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (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 (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> False). % 8.61/8.83 do 0 intro. intros zenon_H35e zenon_H35d zenon_H34d zenon_H36a zenon_H3c zenon_Hed zenon_H98 zenon_H71 zenon_H2a zenon_H9f zenon_H9a zenon_H4c zenon_H1e zenon_H1d9 zenon_H173 zenon_H22d zenon_H1d7 zenon_Ha8 zenon_H192 zenon_Ha3 zenon_H2b8 zenon_H67 zenon_H197 zenon_H2b zenon_Hab zenon_Hc2 zenon_H1f6 zenon_H78 zenon_H127 zenon_H31 zenon_H25 zenon_H22e zenon_H153 zenon_H170 zenon_Hc5 zenon_H3a zenon_H2a2 zenon_H29f zenon_H2d2 zenon_H2d4 zenon_H145 zenon_H10c zenon_Hb4 zenon_H32e zenon_H109 zenon_He7 zenon_Hff zenon_H2d8 zenon_H329 zenon_H2a5 zenon_H129 zenon_H12b zenon_H2fc zenon_H36 zenon_H11f zenon_H124 zenon_H2bf zenon_H2e2 zenon_H1dd zenon_H164 zenon_Hf8 zenon_H2a3 zenon_Hf9 zenon_Hf3 zenon_H285 zenon_H2e8 zenon_H27f zenon_H137 zenon_H282 zenon_H150 zenon_H74 zenon_H6c zenon_Hb7 zenon_H2c9 zenon_H19a zenon_H295 zenon_H2a1 zenon_H1dc zenon_H169 zenon_H2c0 zenon_H2b5 zenon_H2a4 zenon_H270 zenon_H1f zenon_H16d zenon_Hd0 zenon_H2f3 zenon_H2df zenon_H1d3 zenon_H105 zenon_H322 zenon_He4 zenon_Hbf zenon_H303 zenon_Hba zenon_H331 zenon_H11e zenon_Heb zenon_H94 zenon_H336 zenon_H134 zenon_H2f8 zenon_H300 zenon_H90 zenon_H7d. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.61/8.83 apply (zenon_L17_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.61/8.83 apply (zenon_L639_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.61/8.83 apply (zenon_L21_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.61/8.83 apply (zenon_L21_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.61/8.83 apply (zenon_L641_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.61/8.83 apply (zenon_L44_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.61/8.83 apply (zenon_L641_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.61/8.83 apply (zenon_L46_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.61/8.83 apply (zenon_L30_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.61/8.83 apply (zenon_L31_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.61/8.83 apply (zenon_L32_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.61/8.83 apply (zenon_L4_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.61/8.83 apply (zenon_L642_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.61/8.83 apply (zenon_L65_); trivial. % 8.61/8.83 apply (zenon_L69_); trivial. % 8.61/8.83 apply (zenon_L63_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.61/8.83 apply (zenon_L23_); trivial. % 8.61/8.83 apply (zenon_L59_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.61/8.83 apply (zenon_L21_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.61/8.83 apply (zenon_L641_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.61/8.83 apply (zenon_L495_); trivial. % 8.61/8.83 apply (zenon_L55_); trivial. % 8.61/8.83 (* end of lemma zenon_L643_ *) % 8.61/8.83 assert (zenon_L644_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> False). % 8.61/8.83 do 0 intro. intros zenon_Hbf zenon_H71 zenon_H7d zenon_Hab zenon_Hb0 zenon_H3c zenon_H3a zenon_H65. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H7e | zenon_intro zenon_Hc0 ]. % 8.61/8.83 apply (zenon_L23_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H93 | zenon_intro zenon_Hc1 ]. % 8.61/8.83 apply (zenon_L34_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H3b | zenon_intro zenon_Hbd ]. % 8.61/8.83 apply (zenon_L6_); trivial. % 8.61/8.83 apply (zenon_L295_); trivial. % 8.61/8.83 (* end of lemma zenon_L644_ *) % 8.61/8.83 assert (zenon_L645_ : (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e1)) = (e0)) -> False). % 8.61/8.83 do 0 intro. intros zenon_H64 zenon_Hf0 zenon_H1df. % 8.61/8.83 cut (((op (e3) (e0)) = (e1)) = ((op (e3) (op (e3) (e1))) = (e1))). % 8.61/8.83 intro zenon_D_pnotp. % 8.61/8.83 apply zenon_H64. % 8.61/8.83 rewrite <- zenon_D_pnotp. % 8.61/8.83 exact zenon_Hf0. % 8.61/8.83 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.61/8.83 cut (((op (e3) (e0)) = (op (e3) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H36e]. % 8.61/8.83 congruence. % 8.61/8.83 elim (classic ((op (e3) (op (e3) (e1))) = (op (e3) (op (e3) (e1))))); [ zenon_intro zenon_H29b | zenon_intro zenon_H29c ]. % 8.61/8.83 cut (((op (e3) (op (e3) (e1))) = (op (e3) (op (e3) (e1)))) = ((op (e3) (e0)) = (op (e3) (op (e3) (e1))))). % 8.61/8.83 intro zenon_D_pnotp. % 8.61/8.83 apply zenon_H36e. % 8.61/8.83 rewrite <- zenon_D_pnotp. % 8.61/8.83 exact zenon_H29b. % 8.61/8.83 cut (((op (e3) (op (e3) (e1))) = (op (e3) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H29c]. % 8.61/8.83 cut (((op (e3) (op (e3) (e1))) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H36f]. % 8.61/8.83 congruence. % 8.61/8.83 cut (((op (e3) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H370]. % 8.61/8.83 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.61/8.83 congruence. % 8.61/8.83 apply zenon_H58. apply refl_equal. % 8.61/8.83 exact (zenon_H370 zenon_H1df). % 8.61/8.83 apply zenon_H29c. apply refl_equal. % 8.61/8.83 apply zenon_H29c. apply refl_equal. % 8.61/8.83 apply zenon_H40. apply refl_equal. % 8.61/8.83 (* end of lemma zenon_L645_ *) % 8.61/8.83 assert (zenon_L646_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 8.61/8.83 do 0 intro. intros zenon_Hf9 zenon_H1df zenon_H64 zenon_H2a zenon_Hf3 zenon_H98 zenon_Ha3 zenon_He4 zenon_Hd6. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hfc ]. % 8.61/8.83 apply (zenon_L645_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hfd ]. % 8.61/8.83 apply (zenon_L56_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_Hf6 | zenon_intro zenon_He5 ]. % 8.61/8.83 apply (zenon_L57_); trivial. % 8.61/8.83 apply (zenon_L51_); trivial. % 8.61/8.83 (* end of lemma zenon_L646_ *) % 8.61/8.83 assert (zenon_L647_ : (((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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 8.61/8.83 do 0 intro. intros zenon_H2d4 zenon_H1df zenon_H1d9 zenon_H71 zenon_H29f zenon_H65 zenon_Ha7 zenon_H2d2. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H2d5 ]. % 8.61/8.83 apply (zenon_L573_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H2d6 ]. % 8.61/8.83 apply (zenon_L266_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_Hbd | zenon_intro zenon_H98 ]. % 8.61/8.83 apply (zenon_L295_); trivial. % 8.61/8.83 apply (zenon_L358_); trivial. % 8.61/8.83 (* end of lemma zenon_L647_ *) % 8.61/8.83 assert (zenon_L648_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 8.61/8.83 do 0 intro. intros zenon_Hba zenon_H9a zenon_H98 zenon_H93 zenon_H94 zenon_H90 zenon_H9f zenon_Ha3 zenon_H2a zenon_H2d2 zenon_H65 zenon_H29f zenon_H71 zenon_H1d9 zenon_H1df zenon_H2d4 zenon_Hd0 zenon_H103. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.61/8.83 apply (zenon_L30_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.61/8.83 apply (zenon_L31_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.61/8.83 apply (zenon_L647_); trivial. % 8.61/8.83 apply (zenon_L60_); trivial. % 8.61/8.83 (* end of lemma zenon_L648_ *) % 8.61/8.83 assert (zenon_L649_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 8.61/8.83 do 0 intro. intros zenon_H105 zenon_Hd1 zenon_He4 zenon_Hf3 zenon_H64 zenon_Hf9 zenon_Hff zenon_H3c zenon_Hba zenon_H9a zenon_H98 zenon_H93 zenon_H94 zenon_H90 zenon_H9f zenon_Ha3 zenon_H2a zenon_H2d2 zenon_H65 zenon_H29f zenon_H71 zenon_H1d9 zenon_H1df zenon_H2d4 zenon_Hd0. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H30 | zenon_intro zenon_H106 ]. % 8.61/8.83 apply (zenon_L47_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H107 ]. % 8.61/8.83 apply (zenon_L646_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfe | zenon_intro zenon_H103 ]. % 8.61/8.83 apply (zenon_L59_); trivial. % 8.61/8.83 apply (zenon_L648_); trivial. % 8.61/8.83 (* end of lemma zenon_L649_ *) % 8.61/8.83 assert (zenon_L650_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 8.61/8.83 do 0 intro. intros zenon_H10c zenon_H3a zenon_Hab zenon_Hbf zenon_H7d zenon_Hd0 zenon_H2d4 zenon_H1df zenon_H1d9 zenon_H71 zenon_H29f zenon_H65 zenon_H2d2 zenon_H2a zenon_Ha3 zenon_H9f zenon_H90 zenon_H94 zenon_H98 zenon_H9a zenon_Hba zenon_Hff zenon_Hf9 zenon_H64 zenon_Hf3 zenon_He4 zenon_Hd1 zenon_H105 zenon_H3c zenon_H109. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.61/8.83 apply (zenon_L644_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.61/8.83 apply (zenon_L46_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.61/8.83 apply (zenon_L649_); trivial. % 8.61/8.83 apply (zenon_L63_); trivial. % 8.61/8.83 (* end of lemma zenon_L650_ *) % 8.61/8.83 assert (zenon_L651_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.61/8.83 do 0 intro. intros zenon_H11e zenon_H109 zenon_Ha8 zenon_H371 zenon_H62 zenon_H78 zenon_H10c zenon_H3a zenon_Hab zenon_Hbf zenon_H2d4 zenon_H1d9 zenon_H29f zenon_H65 zenon_H2d2 zenon_H9f zenon_H90 zenon_H94 zenon_H9a zenon_Hba zenon_H64 zenon_H1e zenon_H31 zenon_H11f zenon_Hc2 zenon_Hf9 zenon_H2a zenon_Hf3 zenon_H98 zenon_Ha3 zenon_H105 zenon_He4 zenon_Hc9 zenon_Hd0 zenon_H6c zenon_Hf8 zenon_H71 zenon_H7d zenon_H3c zenon_Hff. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.61/8.83 apply (zenon_L21_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.61/8.83 apply (zenon_L21_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.61/8.83 apply (zenon_L644_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.61/8.83 apply (zenon_L44_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.61/8.83 apply (zenon_L644_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.61/8.83 apply (zenon_L45_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.61/8.83 apply (zenon_L30_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.61/8.83 apply (zenon_L31_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.61/8.83 apply (zenon_L32_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H371); [ zenon_intro zenon_H14e | zenon_intro zenon_H372 ]. % 8.61/8.83 apply (zenon_L416_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H372); [ zenon_intro zenon_H1df | zenon_intro zenon_H373 ]. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.61/8.83 apply (zenon_L4_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.61/8.83 apply (zenon_L650_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.61/8.83 apply (zenon_L65_); trivial. % 8.61/8.83 apply (zenon_L69_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H373); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hd4 ]. % 8.61/8.83 apply (zenon_L42_); trivial. % 8.61/8.83 apply (zenon_L69_); trivial. % 8.61/8.83 apply (zenon_L63_); trivial. % 8.61/8.83 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.61/8.83 apply (zenon_L23_); trivial. % 8.61/8.83 apply (zenon_L59_); trivial. % 8.61/8.83 (* end of lemma zenon_L651_ *) % 8.61/8.83 assert (zenon_L652_ : ((op (e0) (e0)) = (e0)) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (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 (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 8.61/8.84 do 0 intro. intros zenon_H1e zenon_H65 zenon_H3c zenon_H71 zenon_H1d9 zenon_H173 zenon_H22d zenon_H1d7 zenon_Ha8 zenon_H192 zenon_Ha3 zenon_H2b8 zenon_H67 zenon_H197 zenon_H2b zenon_Hab zenon_Hc2 zenon_H1f6 zenon_H78 zenon_H127 zenon_H31 zenon_H25 zenon_H22e zenon_H153 zenon_H170 zenon_Hc5 zenon_H3a zenon_H2a2 zenon_H29f zenon_H2d2 zenon_H2d4 zenon_H145 zenon_H10c zenon_Hb4 zenon_H32e zenon_H109 zenon_He7 zenon_Hff zenon_H2d8 zenon_H329 zenon_H2a5 zenon_H129 zenon_H12b zenon_H2fc zenon_H36 zenon_H11f zenon_H124 zenon_H2bf zenon_H2e2 zenon_H1dd zenon_H164 zenon_Hf8 zenon_H2a3 zenon_Hf9 zenon_Hf3 zenon_H285 zenon_H2e8 zenon_H27f zenon_H137 zenon_H282 zenon_H150 zenon_H74 zenon_H6c zenon_Hb7 zenon_H2c9 zenon_H19a zenon_H295 zenon_H2a1 zenon_H1dc zenon_H169 zenon_H2c0 zenon_H2b5 zenon_H2a4 zenon_H270 zenon_H1f zenon_H16d zenon_Hd0 zenon_H2f3 zenon_H2df zenon_H1d3 zenon_H105 zenon_H322 zenon_He4 zenon_Hbf zenon_H303 zenon_Hba zenon_H331 zenon_H11e zenon_Heb zenon_H94 zenon_H336 zenon_H134 zenon_H2f8 zenon_H300 zenon_H90 zenon_Hf0 zenon_H7d. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.61/8.84 apply (zenon_L21_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.61/8.84 apply (zenon_L644_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.61/8.84 apply (zenon_L495_); trivial. % 8.61/8.84 apply (zenon_L55_); trivial. % 8.61/8.84 (* end of lemma zenon_L652_ *) % 8.61/8.84 assert (zenon_L653_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> False). % 8.61/8.84 do 0 intro. intros zenon_H371 zenon_H67 zenon_Hf0 zenon_H64 zenon_H98 zenon_Hc2 zenon_Hb0 zenon_Hd6. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H371); [ zenon_intro zenon_H14e | zenon_intro zenon_H372 ]. % 8.61/8.84 apply (zenon_L94_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H372); [ zenon_intro zenon_H1df | zenon_intro zenon_H373 ]. % 8.61/8.84 apply (zenon_L645_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H373); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hd4 ]. % 8.61/8.84 apply (zenon_L42_); trivial. % 8.61/8.84 apply (zenon_L50_); trivial. % 8.61/8.84 (* end of lemma zenon_L653_ *) % 8.61/8.84 assert (zenon_L654_ : ((op (e0) (e0)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((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 (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) 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(~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (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 (e3) (e0)))) -> (((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 8.61/8.84 do 0 intro. intros zenon_H1e zenon_Hd6 zenon_H98 zenon_H64 zenon_H371 zenon_Heb zenon_H12b zenon_H2a zenon_H36 zenon_H2a5 zenon_H2a4 zenon_H29f zenon_H137 zenon_H11e zenon_H331 zenon_Hb4 zenon_Hc5 zenon_H153 zenon_Hab zenon_H74 zenon_Hb7 zenon_H170 zenon_H145 zenon_H10c zenon_H2a2 zenon_H31 zenon_Hba zenon_Hc2 zenon_Ha3 zenon_H2d2 zenon_Ha8 zenon_H329 zenon_H78 zenon_H22d zenon_H173 zenon_H2b zenon_H1d9 zenon_H1d7 zenon_H192 zenon_H2b8 zenon_H197 zenon_H1f6 zenon_H127 zenon_H25 zenon_H22e zenon_H3a zenon_H2d4 zenon_H32e zenon_H109 zenon_He7 zenon_Hff zenon_H2d8 zenon_H129 zenon_H2fc zenon_H11f zenon_H124 zenon_H2bf zenon_H2e2 zenon_H1dd zenon_H164 zenon_Hf8 zenon_H2a3 zenon_Hf9 zenon_Hf3 zenon_H285 zenon_H2e8 zenon_H282 zenon_H2c9 zenon_H19a zenon_H295 zenon_H1dc zenon_H169 zenon_H2c0 zenon_H2b5 zenon_H270 zenon_H1f zenon_H2f3 zenon_H2df zenon_H1d3 zenon_H303 zenon_Hbf zenon_H2a1 zenon_He4 zenon_H16d zenon_H27f zenon_H322 zenon_Hd0 zenon_H105 zenon_H6c zenon_H150 zenon_H67 zenon_Hf0 zenon_H7d. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.61/8.84 apply (zenon_L21_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.61/8.84 apply (zenon_L653_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.61/8.84 apply (zenon_L494_); trivial. % 8.61/8.84 apply (zenon_L55_); trivial. % 8.61/8.84 (* end of lemma zenon_L654_ *) % 8.61/8.84 assert (zenon_L655_ : (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (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) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((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 (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 8.61/8.84 do 0 intro. intros zenon_H7d zenon_H67 zenon_H150 zenon_H6c zenon_H105 zenon_Hd0 zenon_H322 zenon_H27f zenon_H16d zenon_H2a1 zenon_Hbf zenon_H303 zenon_H1d3 zenon_H2df zenon_H2f3 zenon_H1f zenon_H270 zenon_H2b5 zenon_H2c0 zenon_H169 zenon_H1dc zenon_H295 zenon_H19a zenon_H2c9 zenon_H282 zenon_H2e8 zenon_H285 zenon_Hf3 zenon_Hf9 zenon_H2a3 zenon_Hf8 zenon_H164 zenon_H1dd zenon_H2e2 zenon_H2bf zenon_H124 zenon_H11f zenon_H2fc zenon_H129 zenon_H2d8 zenon_Hff zenon_He7 zenon_H109 zenon_H32e zenon_H2d4 zenon_H3a zenon_H22e zenon_H25 zenon_H127 zenon_H1f6 zenon_H197 zenon_H2b8 zenon_H192 zenon_H1d7 zenon_H1d9 zenon_H2b zenon_H173 zenon_H22d zenon_H78 zenon_H329 zenon_Ha8 zenon_H2d2 zenon_Hc2 zenon_Hba zenon_H31 zenon_H2a2 zenon_H10c zenon_H145 zenon_H170 zenon_Hb7 zenon_H74 zenon_Hab zenon_H153 zenon_Hc5 zenon_Hb4 zenon_H331 zenon_H11e zenon_H137 zenon_H29f zenon_H2a4 zenon_H2a5 zenon_H36 zenon_H2a zenon_H12b zenon_Heb zenon_H371 zenon_H1e zenon_H64 zenon_H98 zenon_Ha3 zenon_He4 zenon_Hd6. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hfc ]. % 8.61/8.84 apply (zenon_L654_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hfd ]. % 8.61/8.84 apply (zenon_L265_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_Hf6 | zenon_intro zenon_He5 ]. % 8.61/8.84 apply (zenon_L57_); trivial. % 8.61/8.84 apply (zenon_L51_); trivial. % 8.61/8.84 (* end of lemma zenon_L655_ *) % 8.61/8.84 assert (zenon_L656_ : ((op (e0) (e1)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> False). % 8.61/8.84 do 0 intro. intros zenon_H6b zenon_Hcb zenon_H7d. % 8.61/8.84 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H79 | zenon_intro zenon_H4b ]. % 8.61/8.84 cut (((e2) = (e2)) = ((e1) = (e2))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_H7d. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_H79. % 8.61/8.84 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.61/8.84 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hce]. % 8.61/8.84 congruence. % 8.61/8.84 cut (((op (e0) (e1)) = (e1)) = ((e2) = (e1))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_Hce. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_H6b. % 8.61/8.84 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.61/8.84 cut (((op (e0) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H13c]. % 8.61/8.84 congruence. % 8.61/8.84 exact (zenon_H13c zenon_Hcb). % 8.61/8.84 apply zenon_H40. apply refl_equal. % 8.61/8.84 apply zenon_H4b. apply refl_equal. % 8.61/8.84 apply zenon_H4b. apply refl_equal. % 8.61/8.84 (* end of lemma zenon_L656_ *) % 8.61/8.84 assert (zenon_L657_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 8.61/8.84 do 0 intro. intros zenon_H322 zenon_H7d zenon_Hf0 zenon_H191 zenon_H169 zenon_H29f zenon_H7e zenon_Ha8 zenon_H5a. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H323 ]. % 8.61/8.84 apply (zenon_L55_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H324 ]. % 8.61/8.84 apply (zenon_L628_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_Hbd | zenon_intro zenon_He8 ]. % 8.61/8.84 apply (zenon_L398_); trivial. % 8.61/8.84 apply (zenon_L439_); trivial. % 8.61/8.84 (* end of lemma zenon_L657_ *) % 8.61/8.84 assert (zenon_L658_ : (~((op (op (e1) (e1)) (e1)) = (op (e0) (e1)))) -> ((op (e1) (e1)) = (e0)) -> False). % 8.61/8.84 do 0 intro. intros zenon_H374 zenon_H358. % 8.61/8.84 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.61/8.84 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H35b]. % 8.61/8.84 congruence. % 8.61/8.84 exact (zenon_H35b zenon_H358). % 8.61/8.84 apply zenon_H40. apply refl_equal. % 8.61/8.84 (* end of lemma zenon_L658_ *) % 8.61/8.84 assert (zenon_L659_ : ((op (e0) (e1)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((e3) = (op (op (e1) (e1)) (e1)))) -> False). % 8.61/8.84 do 0 intro. intros zenon_H274 zenon_H358 zenon_H33c. % 8.61/8.84 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H33d | zenon_intro zenon_H33e ]. % 8.61/8.84 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e3) = (op (op (e1) (e1)) (e1)))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_H33c. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_H33d. % 8.61/8.84 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H33e]. % 8.61/8.84 cut (((op (op (e1) (e1)) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H33f]. % 8.61/8.84 congruence. % 8.61/8.84 cut (((op (e0) (e1)) = (e3)) = ((op (op (e1) (e1)) (e1)) = (e3))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_H33f. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_H274. % 8.61/8.84 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.61/8.84 cut (((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H375]. % 8.61/8.84 congruence. % 8.61/8.84 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H33d | zenon_intro zenon_H33e ]. % 8.61/8.84 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_H375. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_H33d. % 8.61/8.84 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H33e]. % 8.61/8.84 cut (((op (op (e1) (e1)) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H374]. % 8.61/8.84 congruence. % 8.61/8.84 apply (zenon_L658_); trivial. % 8.61/8.84 apply zenon_H33e. apply refl_equal. % 8.61/8.84 apply zenon_H33e. apply refl_equal. % 8.61/8.84 apply zenon_H58. apply refl_equal. % 8.61/8.84 apply zenon_H33e. apply refl_equal. % 8.61/8.84 apply zenon_H33e. apply refl_equal. % 8.61/8.84 (* end of lemma zenon_L659_ *) % 8.61/8.84 assert (zenon_L660_ : ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> False). % 8.61/8.84 do 0 intro. intros zenon_Hf1 zenon_H274 zenon_H358. % 8.61/8.84 apply (zenon_notand_s _ _ ax6); [ zenon_intro zenon_H377 | zenon_intro zenon_H376 ]. % 8.61/8.84 apply zenon_H377. apply sym_equal. exact zenon_H358. % 8.61/8.84 apply (zenon_notand_s _ _ zenon_H376); [ zenon_intro zenon_H378 | zenon_intro zenon_H33c ]. % 8.61/8.84 elim (classic ((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H343 | zenon_intro zenon_H344 ]. % 8.61/8.84 cut (((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1)))) = ((e2) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_H378. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_H343. % 8.61/8.84 cut (((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H344]. % 8.61/8.84 cut (((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H379]. % 8.61/8.84 congruence. % 8.61/8.84 cut (((op (e3) (e0)) = (e2)) = ((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (e2))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_H379. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_Hf1. % 8.61/8.84 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.61/8.84 cut (((op (e3) (e0)) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H37a]. % 8.61/8.84 congruence. % 8.61/8.84 elim (classic ((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H343 | zenon_intro zenon_H344 ]. % 8.61/8.84 cut (((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1)))) = ((op (e3) (e0)) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_H37a. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_H343. % 8.61/8.84 cut (((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H344]. % 8.61/8.84 cut (((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H37b]. % 8.61/8.84 congruence. % 8.61/8.84 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H35b]. % 8.61/8.84 cut (((op (op (e1) (e1)) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H33f]. % 8.61/8.84 congruence. % 8.61/8.84 cut (((op (e0) (e1)) = (e3)) = ((op (op (e1) (e1)) (e1)) = (e3))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_H33f. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_H274. % 8.61/8.84 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.61/8.84 cut (((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H375]. % 8.61/8.84 congruence. % 8.61/8.84 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H33d | zenon_intro zenon_H33e ]. % 8.61/8.84 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_H375. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_H33d. % 8.61/8.84 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H33e]. % 8.61/8.84 cut (((op (op (e1) (e1)) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H374]. % 8.61/8.84 congruence. % 8.61/8.84 apply (zenon_L658_); trivial. % 8.61/8.84 apply zenon_H33e. apply refl_equal. % 8.61/8.84 apply zenon_H33e. apply refl_equal. % 8.61/8.84 apply zenon_H58. apply refl_equal. % 8.61/8.84 exact (zenon_H35b zenon_H358). % 8.61/8.84 apply zenon_H344. apply refl_equal. % 8.61/8.84 apply zenon_H344. apply refl_equal. % 8.61/8.84 apply zenon_H4b. apply refl_equal. % 8.61/8.84 apply zenon_H344. apply refl_equal. % 8.61/8.84 apply zenon_H344. apply refl_equal. % 8.61/8.84 apply (zenon_L659_); trivial. % 8.61/8.84 (* end of lemma zenon_L660_ *) % 8.61/8.84 assert (zenon_L661_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 8.61/8.84 do 0 intro. intros zenon_H2e2 zenon_H1f zenon_H1e zenon_H1dd zenon_Hf4 zenon_H164 zenon_H191 zenon_Hf1 zenon_H358. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H1d | zenon_intro zenon_H2e3 ]. % 8.61/8.84 apply (zenon_L1_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H6b | zenon_intro zenon_H2e4 ]. % 8.61/8.84 apply (zenon_L313_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_Hcb | zenon_intro zenon_H274 ]. % 8.61/8.84 apply (zenon_L314_); trivial. % 8.61/8.84 apply (zenon_L660_); trivial. % 8.61/8.84 (* end of lemma zenon_L661_ *) % 8.61/8.84 assert (zenon_L662_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 8.61/8.84 do 0 intro. intros zenon_H322 zenon_H358 zenon_H164 zenon_Hf4 zenon_H1dd zenon_H1e zenon_H1f zenon_H2e2 zenon_H191 zenon_H169 zenon_H29f zenon_H7e zenon_Ha8 zenon_H5a. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H323 ]. % 8.61/8.84 apply (zenon_L661_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H324 ]. % 8.61/8.84 apply (zenon_L628_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_Hbd | zenon_intro zenon_He8 ]. % 8.61/8.84 apply (zenon_L398_); trivial. % 8.61/8.84 apply (zenon_L439_); trivial. % 8.61/8.84 (* end of lemma zenon_L662_ *) % 8.61/8.84 assert (zenon_L663_ : (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> False). % 8.61/8.84 do 0 intro. intros zenon_Ha3 zenon_H5a zenon_He5. % 8.61/8.84 cut (((op (e3) (e3)) = (e3)) = ((e1) = (e3))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_Ha3. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_H5a. % 8.61/8.84 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.61/8.84 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2ec]. % 8.61/8.84 congruence. % 8.61/8.84 exact (zenon_H2ec zenon_He5). % 8.61/8.84 apply zenon_H58. apply refl_equal. % 8.61/8.84 (* end of lemma zenon_L663_ *) % 8.61/8.84 assert (zenon_L664_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 8.61/8.84 do 0 intro. intros zenon_Hf9 zenon_H7d zenon_Ha8 zenon_H7e zenon_H29f zenon_H169 zenon_H191 zenon_H2e2 zenon_H1f zenon_H1e zenon_H1dd zenon_H164 zenon_H358 zenon_H322 zenon_H29 zenon_H2d2 zenon_Ha3 zenon_H5a. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hfc ]. % 8.61/8.84 apply (zenon_L657_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hfd ]. % 8.61/8.84 apply (zenon_L662_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_Hf6 | zenon_intro zenon_He5 ]. % 8.61/8.84 apply (zenon_L466_); trivial. % 8.61/8.84 apply (zenon_L663_); trivial. % 8.61/8.84 (* end of lemma zenon_L664_ *) % 8.61/8.84 assert (zenon_L665_ : ((op (e0) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> (~((e3) = (op (op (e2) (e2)) (e2)))) -> False). % 8.61/8.84 do 0 intro. intros zenon_H276 zenon_H80 zenon_H310. % 8.61/8.84 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H83 | zenon_intro zenon_H84 ]. % 8.61/8.84 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e3) = (op (op (e2) (e2)) (e2)))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_H310. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_H83. % 8.61/8.84 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 8.61/8.84 cut (((op (op (e2) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H311]. % 8.61/8.84 congruence. % 8.61/8.84 cut (((op (e0) (e2)) = (e3)) = ((op (op (e2) (e2)) (e2)) = (e3))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_H311. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_H276. % 8.61/8.84 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.61/8.84 cut (((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 8.61/8.84 congruence. % 8.61/8.84 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H83 | zenon_intro zenon_H84 ]. % 8.61/8.84 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_H86. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_H83. % 8.61/8.84 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 8.61/8.84 cut (((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 8.61/8.84 congruence. % 8.61/8.84 apply (zenon_L24_); trivial. % 8.61/8.84 apply zenon_H84. apply refl_equal. % 8.61/8.84 apply zenon_H84. apply refl_equal. % 8.61/8.84 apply zenon_H58. apply refl_equal. % 8.61/8.84 apply zenon_H84. apply refl_equal. % 8.61/8.84 apply zenon_H84. apply refl_equal. % 8.61/8.84 (* end of lemma zenon_L665_ *) % 8.61/8.84 assert (zenon_L666_ : ((op (e3) (e0)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> False). % 8.61/8.84 do 0 intro. intros zenon_Hf0 zenon_H276 zenon_H80. % 8.61/8.84 apply (zenon_notand_s _ _ ax8); [ zenon_intro zenon_H89 | zenon_intro zenon_H37c ]. % 8.61/8.84 apply zenon_H89. apply sym_equal. exact zenon_H80. % 8.61/8.84 apply (zenon_notand_s _ _ zenon_H37c); [ zenon_intro zenon_H37d | zenon_intro zenon_H310 ]. % 8.61/8.84 elim (classic ((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ]. % 8.61/8.84 cut (((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2)))) = ((e1) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_H37d. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_H8b. % 8.61/8.84 cut (((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 8.61/8.84 cut (((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H37e]. % 8.61/8.84 congruence. % 8.61/8.84 cut (((op (e3) (e0)) = (e1)) = ((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (e1))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_H37e. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_Hf0. % 8.61/8.84 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.61/8.84 cut (((op (e3) (e0)) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H37f]. % 8.61/8.84 congruence. % 8.61/8.84 elim (classic ((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H8b | zenon_intro zenon_H8c ]. % 8.61/8.84 cut (((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2)))) = ((op (e3) (e0)) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_H37f. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_H8b. % 8.61/8.84 cut (((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (op (op (e2) (e2)) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 8.61/8.84 cut (((op (op (op (e2) (e2)) (e2)) (op (e2) (e2))) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H380]. % 8.61/8.84 congruence. % 8.61/8.84 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 8.61/8.84 cut (((op (op (e2) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H311]. % 8.61/8.84 congruence. % 8.61/8.84 cut (((op (e0) (e2)) = (e3)) = ((op (op (e2) (e2)) (e2)) = (e3))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_H311. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_H276. % 8.61/8.84 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.61/8.84 cut (((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 8.61/8.84 congruence. % 8.61/8.84 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H83 | zenon_intro zenon_H84 ]. % 8.61/8.84 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_H86. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_H83. % 8.61/8.84 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 8.61/8.84 cut (((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 8.61/8.84 congruence. % 8.61/8.84 apply (zenon_L24_); trivial. % 8.61/8.84 apply zenon_H84. apply refl_equal. % 8.61/8.84 apply zenon_H84. apply refl_equal. % 8.61/8.84 apply zenon_H58. apply refl_equal. % 8.61/8.84 exact (zenon_H81 zenon_H80). % 8.61/8.84 apply zenon_H8c. apply refl_equal. % 8.61/8.84 apply zenon_H8c. apply refl_equal. % 8.61/8.84 apply zenon_H40. apply refl_equal. % 8.61/8.84 apply zenon_H8c. apply refl_equal. % 8.61/8.84 apply zenon_H8c. apply refl_equal. % 8.61/8.84 apply (zenon_L665_); trivial. % 8.61/8.84 (* end of lemma zenon_L666_ *) % 8.61/8.84 assert (zenon_L667_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> False). % 8.61/8.84 do 0 intro. intros zenon_H300 zenon_H25 zenon_H1e zenon_H134 zenon_H29 zenon_H5a zenon_Ha8 zenon_H29f zenon_H169 zenon_H191 zenon_H7d zenon_H322 zenon_Hf0 zenon_H80. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H24 | zenon_intro zenon_H301 ]. % 8.61/8.84 apply (zenon_L2_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H71 | zenon_intro zenon_H302 ]. % 8.61/8.84 apply (zenon_L78_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H7e | zenon_intro zenon_H276 ]. % 8.61/8.84 apply (zenon_L657_); trivial. % 8.61/8.84 apply (zenon_L666_); trivial. % 8.61/8.84 (* end of lemma zenon_L667_ *) % 8.61/8.84 assert (zenon_L668_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 8.61/8.84 do 0 intro. intros zenon_Hf9 zenon_H80 zenon_H322 zenon_H7d zenon_H191 zenon_H169 zenon_H29f zenon_Ha8 zenon_H134 zenon_H1e zenon_H25 zenon_H300 zenon_H1dd zenon_H6b zenon_H29 zenon_H2d2 zenon_Ha3 zenon_H5a. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hfc ]. % 8.61/8.84 apply (zenon_L667_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hfd ]. % 8.61/8.84 apply (zenon_L313_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_Hf6 | zenon_intro zenon_He5 ]. % 8.61/8.84 apply (zenon_L466_); trivial. % 8.61/8.84 apply (zenon_L663_); trivial. % 8.61/8.84 (* end of lemma zenon_L668_ *) % 8.61/8.84 assert (zenon_L669_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> False). % 8.61/8.84 do 0 intro. intros zenon_Hc5 zenon_H78 zenon_H7e zenon_H67 zenon_H5a zenon_Ha3 zenon_H2d2 zenon_H29 zenon_H6b zenon_H1dd zenon_H300 zenon_H25 zenon_H1e zenon_H134 zenon_Ha8 zenon_H29f zenon_H169 zenon_H191 zenon_H7d zenon_H322 zenon_Hf9 zenon_H1d9 zenon_H1df. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_H24 | zenon_intro zenon_Hc6 ]. % 8.61/8.84 apply (zenon_L128_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Had | zenon_intro zenon_Hc7 ]. % 8.61/8.84 apply (zenon_L110_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H80 | zenon_intro zenon_Hc3 ]. % 8.61/8.84 apply (zenon_L668_); trivial. % 8.61/8.84 apply (zenon_L573_); trivial. % 8.61/8.84 (* end of lemma zenon_L669_ *) % 8.61/8.84 assert (zenon_L670_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.61/8.84 do 0 intro. intros zenon_H35e zenon_H164 zenon_H1f zenon_H2e2 zenon_Hc5 zenon_H78 zenon_H7e zenon_H67 zenon_H5a zenon_Ha3 zenon_H2d2 zenon_H29 zenon_H6b zenon_H1dd zenon_H300 zenon_H25 zenon_H1e zenon_H134 zenon_Ha8 zenon_H29f zenon_H169 zenon_H191 zenon_H7d zenon_H322 zenon_Hf9 zenon_H1d9. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.61/8.84 apply (zenon_L77_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.61/8.84 apply (zenon_L664_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.61/8.84 apply (zenon_L626_); trivial. % 8.61/8.84 apply (zenon_L669_); trivial. % 8.61/8.84 (* end of lemma zenon_L670_ *) % 8.61/8.84 assert (zenon_L671_ : (((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 (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 8.61/8.84 do 0 intro. intros zenon_H2b5 zenon_H109 zenon_He4 zenon_Hd0 zenon_Hff zenon_H16b zenon_H10f zenon_H105 zenon_H5a zenon_H16d. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H2b6 ]. % 8.61/8.84 apply (zenon_L500_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H35 | zenon_intro zenon_H2b7 ]. % 8.61/8.84 apply (zenon_L106_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H108 | zenon_intro zenon_Hb3 ]. % 8.61/8.84 apply (zenon_L108_); trivial. % 8.61/8.84 apply (zenon_L109_); trivial. % 8.61/8.84 (* end of lemma zenon_L671_ *) % 8.61/8.84 assert (zenon_L672_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (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)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 8.61/8.84 do 0 intro. intros zenon_H2b8 zenon_H7d zenon_H29 zenon_H129 zenon_H105 zenon_Hff zenon_He4 zenon_H2b5 zenon_H10f zenon_H109 zenon_Hfe zenon_Hd0 zenon_H5a zenon_H16d. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H2b9 ]. % 8.61/8.84 apply (zenon_L81_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_H35 | zenon_intro zenon_H2ba ]. % 8.61/8.84 apply (zenon_L74_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H16b | zenon_intro zenon_He5 ]. % 8.61/8.84 apply (zenon_L671_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H2b6 ]. % 8.61/8.84 apply (zenon_L500_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H35 | zenon_intro zenon_H2b7 ]. % 8.61/8.84 apply (zenon_L267_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H108 | zenon_intro zenon_Hb3 ]. % 8.61/8.84 apply (zenon_L88_); trivial. % 8.61/8.84 apply (zenon_L109_); trivial. % 8.61/8.84 (* end of lemma zenon_L672_ *) % 8.61/8.84 assert (zenon_L673_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> False). % 8.61/8.84 do 0 intro. intros zenon_H137 zenon_H1e zenon_H143. % 8.61/8.84 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_H137. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_H1e. % 8.61/8.84 cut (((e0) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H381]. % 8.61/8.84 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H27d]. % 8.61/8.84 congruence. % 8.61/8.84 apply zenon_H27d. apply refl_equal. % 8.61/8.84 apply zenon_H381. apply sym_equal. exact zenon_H143. % 8.61/8.84 (* end of lemma zenon_L673_ *) % 8.61/8.84 assert (zenon_L674_ : ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 8.61/8.84 do 0 intro. intros zenon_Hc9 zenon_H27e zenon_Ha3. % 8.61/8.84 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H58 ]. % 8.61/8.84 cut (((e3) = (e3)) = ((e1) = (e3))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_Ha3. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_Ha4. % 8.61/8.84 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.61/8.84 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 8.61/8.84 congruence. % 8.61/8.84 cut (((op (e2) (e0)) = (e1)) = ((e3) = (e1))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_Ha5. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_Hc9. % 8.61/8.84 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.61/8.84 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H328]. % 8.61/8.84 congruence. % 8.61/8.84 exact (zenon_H328 zenon_H27e). % 8.61/8.84 apply zenon_H40. apply refl_equal. % 8.61/8.84 apply zenon_H58. apply refl_equal. % 8.61/8.84 apply zenon_H58. apply refl_equal. % 8.61/8.84 (* end of lemma zenon_L674_ *) % 8.61/8.84 assert (zenon_L675_ : (((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 (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 8.61/8.84 do 0 intro. intros zenon_H2d4 zenon_H1df zenon_H1d9 zenon_H29 zenon_H2d2 zenon_H29f zenon_H7e zenon_H99 zenon_H9a. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H2d5 ]. % 8.61/8.84 apply (zenon_L573_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H2d6 ]. % 8.61/8.84 apply (zenon_L466_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_Hbd | zenon_intro zenon_H98 ]. % 8.61/8.84 apply (zenon_L398_); trivial. % 8.61/8.84 apply (zenon_L29_); trivial. % 8.61/8.84 (* end of lemma zenon_L675_ *) % 8.61/8.84 assert (zenon_L676_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 8.61/8.84 do 0 intro. intros zenon_H36a zenon_Ha3 zenon_Hc9 zenon_Ha8 zenon_H191 zenon_H9a zenon_H7e zenon_H29f zenon_H2d2 zenon_H29 zenon_H1d9 zenon_H1df zenon_H2d4 zenon_H5a zenon_He7. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.61/8.84 apply (zenon_L674_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.61/8.84 apply (zenon_L327_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.61/8.84 apply (zenon_L675_); trivial. % 8.61/8.84 apply (zenon_L501_); trivial. % 8.61/8.84 (* end of lemma zenon_L676_ *) % 8.61/8.84 assert (zenon_L677_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 8.61/8.84 do 0 intro. intros zenon_H11e zenon_H78 zenon_H1e zenon_H164 zenon_H5a zenon_Ha8 zenon_H29f zenon_H169 zenon_H191 zenon_Hf0 zenon_H322 zenon_Hd6 zenon_H7d. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.61/8.84 apply (zenon_L21_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.61/8.84 apply (zenon_L314_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.61/8.84 apply (zenon_L657_); trivial. % 8.61/8.84 apply (zenon_L81_); trivial. % 8.61/8.84 (* end of lemma zenon_L677_ *) % 8.61/8.84 assert (zenon_L678_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 8.61/8.84 do 0 intro. intros zenon_H300 zenon_H1e zenon_H25 zenon_H66 zenon_Hfe zenon_H153 zenon_H98 zenon_H29f. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H24 | zenon_intro zenon_H301 ]. % 8.61/8.84 apply (zenon_L2_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H71 | zenon_intro zenon_H302 ]. % 8.61/8.84 apply (zenon_L19_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H7e | zenon_intro zenon_H276 ]. % 8.61/8.84 apply (zenon_L96_); trivial. % 8.61/8.84 apply (zenon_L399_); trivial. % 8.61/8.84 (* end of lemma zenon_L678_ *) % 8.61/8.84 assert (zenon_L679_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e2)) -> False). % 8.61/8.84 do 0 intro. intros zenon_He4 zenon_Hfe zenon_He8. % 8.61/8.84 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_He4. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_Hfe. % 8.61/8.84 cut (((e2) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He9]. % 8.61/8.84 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 8.61/8.84 congruence. % 8.61/8.84 apply zenon_H33. apply refl_equal. % 8.61/8.84 apply zenon_He9. apply sym_equal. exact zenon_He8. % 8.61/8.84 (* end of lemma zenon_L679_ *) % 8.61/8.84 assert (zenon_L680_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 8.61/8.84 do 0 intro. intros zenon_Hed zenon_Hc9 zenon_H35 zenon_H16d zenon_Hfe zenon_He4 zenon_H195 zenon_He7. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hee ]. % 8.61/8.84 apply (zenon_L68_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_He5 | zenon_intro zenon_Hef ]. % 8.61/8.84 apply (zenon_L267_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hef); [ zenon_intro zenon_He8 | zenon_intro zenon_H5a ]. % 8.61/8.84 apply (zenon_L679_); trivial. % 8.61/8.84 apply (zenon_L501_); trivial. % 8.61/8.84 (* end of lemma zenon_L680_ *) % 8.61/8.84 assert (zenon_L681_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 8.61/8.84 do 0 intro. intros zenon_H11e zenon_H78 zenon_H1e zenon_H164 zenon_H191 zenon_H93 zenon_H134 zenon_Hed zenon_Hc9 zenon_H35 zenon_H16d zenon_He4 zenon_H195 zenon_He7. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.61/8.84 apply (zenon_L21_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.61/8.84 apply (zenon_L314_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.61/8.84 apply (zenon_L86_); trivial. % 8.61/8.84 apply (zenon_L680_); trivial. % 8.61/8.84 (* end of lemma zenon_L681_ *) % 8.61/8.84 assert (zenon_L682_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 8.61/8.84 do 0 intro. intros zenon_H36a zenon_Ha3 zenon_Ha8 zenon_H9a zenon_H98 zenon_H11e zenon_H78 zenon_H1e zenon_H164 zenon_H191 zenon_H93 zenon_H134 zenon_Hed zenon_Hc9 zenon_H35 zenon_H16d zenon_He4 zenon_He7. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.61/8.84 apply (zenon_L674_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.61/8.84 apply (zenon_L327_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.61/8.84 apply (zenon_L29_); trivial. % 8.61/8.84 apply (zenon_L681_); trivial. % 8.61/8.84 (* end of lemma zenon_L682_ *) % 8.61/8.84 assert (zenon_L683_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.61/8.84 do 0 intro. intros zenon_Hbf zenon_H71 zenon_H7d zenon_He7 zenon_He4 zenon_H16d zenon_H35 zenon_Hc9 zenon_Hed zenon_H134 zenon_H164 zenon_H1e zenon_H78 zenon_H11e zenon_H9a zenon_Ha3 zenon_H36a zenon_H191 zenon_H1f6 zenon_Ha8 zenon_H98. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H7e | zenon_intro zenon_Hc0 ]. % 8.61/8.84 apply (zenon_L23_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H93 | zenon_intro zenon_Hc1 ]. % 8.61/8.84 apply (zenon_L682_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H3b | zenon_intro zenon_Hbd ]. % 8.61/8.84 apply (zenon_L198_); trivial. % 8.61/8.84 apply (zenon_L38_); trivial. % 8.61/8.84 (* end of lemma zenon_L683_ *) % 8.61/8.84 assert (zenon_L684_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (op (e0) (e2))) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.61/8.84 do 0 intro. intros zenon_Hbf zenon_H118 zenon_Hab zenon_Hb0 zenon_H91 zenon_H7d zenon_Ha8 zenon_H98. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H7e | zenon_intro zenon_Hc0 ]. % 8.61/8.84 apply (zenon_L70_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H93 | zenon_intro zenon_Hc1 ]. % 8.61/8.84 apply (zenon_L34_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H3b | zenon_intro zenon_Hbd ]. % 8.61/8.84 apply (zenon_L396_); trivial. % 8.61/8.84 apply (zenon_L38_); trivial. % 8.61/8.84 (* end of lemma zenon_L684_ *) % 8.61/8.84 assert (zenon_L685_ : (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> False). % 8.61/8.84 do 0 intro. intros zenon_Hc2 zenon_H1b1 zenon_H1df. % 8.61/8.84 cut (((op (e3) (e1)) = (e3)) = ((e0) = (e3))). % 8.61/8.84 intro zenon_D_pnotp. % 8.61/8.84 apply zenon_Hc2. % 8.61/8.84 rewrite <- zenon_D_pnotp. % 8.61/8.84 exact zenon_H1b1. % 8.61/8.84 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.61/8.84 cut (((op (e3) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H370]. % 8.61/8.84 congruence. % 8.61/8.84 exact (zenon_H370 zenon_H1df). % 8.61/8.84 apply zenon_H58. apply refl_equal. % 8.61/8.84 (* end of lemma zenon_L685_ *) % 8.61/8.84 assert (zenon_L686_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e0)) -> False). % 8.61/8.84 do 0 intro. intros zenon_H2a3 zenon_H127 zenon_H103 zenon_H35 zenon_H41 zenon_Ha8 zenon_H191 zenon_Hc2 zenon_H1df. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H2a3); [ zenon_intro zenon_H274 | zenon_intro zenon_H2b2 ]. % 8.61/8.84 apply (zenon_L315_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H2b3 ]. % 8.61/8.84 apply (zenon_L247_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H196 | zenon_intro zenon_H1b1 ]. % 8.61/8.84 apply (zenon_L327_); trivial. % 8.61/8.84 apply (zenon_L685_); trivial. % 8.61/8.84 (* end of lemma zenon_L686_ *) % 8.61/8.84 assert (zenon_L687_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.61/8.84 do 0 intro. intros zenon_H105 zenon_H10f zenon_Hd0 zenon_H35 zenon_He8 zenon_He4 zenon_Hff zenon_H195. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H30 | zenon_intro zenon_H106 ]. % 8.61/8.84 apply (zenon_L91_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H107 ]. % 8.61/8.84 apply (zenon_L246_); trivial. % 8.61/8.84 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfe | zenon_intro zenon_H103 ]. % 8.61/8.84 apply (zenon_L679_); trivial. % 8.61/8.84 apply (zenon_L324_); trivial. % 8.61/8.84 (* end of lemma zenon_L687_ *) % 8.61/8.84 assert (zenon_L688_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e2)) -> False). % 8.61/8.85 do 0 intro. intros zenon_H331 zenon_H1df zenon_Hc2 zenon_H191 zenon_H41 zenon_H127 zenon_H2a3 zenon_H2c3 zenon_Hff zenon_He4 zenon_H35 zenon_Hd0 zenon_H10f zenon_H105 zenon_Ha8 zenon_He8. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H331); [ zenon_intro zenon_H103 | zenon_intro zenon_H332 ]. % 8.61/8.85 apply (zenon_L686_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H332); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H333 ]. % 8.61/8.85 apply (zenon_L544_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H333); [ zenon_intro zenon_H195 | zenon_intro zenon_H5a ]. % 8.61/8.85 apply (zenon_L687_); trivial. % 8.61/8.85 apply (zenon_L439_); trivial. % 8.61/8.85 (* end of lemma zenon_L688_ *) % 8.61/8.85 assert (zenon_L689_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> False). % 8.61/8.85 do 0 intro. intros zenon_H322 zenon_H7d zenon_Hf0 zenon_H169 zenon_H98 zenon_H331 zenon_H1df zenon_Hc2 zenon_H191 zenon_H41 zenon_H127 zenon_H2a3 zenon_H2c3 zenon_Hff zenon_He4 zenon_H35 zenon_Hd0 zenon_H10f zenon_H105 zenon_Ha8. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H323 ]. % 8.61/8.85 apply (zenon_L55_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H324 ]. % 8.61/8.85 apply (zenon_L628_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_Hbd | zenon_intro zenon_He8 ]. % 8.61/8.85 apply (zenon_L38_); trivial. % 8.61/8.85 apply (zenon_L688_); trivial. % 8.61/8.85 (* end of lemma zenon_L689_ *) % 8.61/8.85 assert (zenon_L690_ : (((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)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.61/8.85 do 0 intro. intros zenon_Hf9 zenon_H7d zenon_Hf1 zenon_H1dd zenon_H6b zenon_H98 zenon_Ha3 zenon_H16d zenon_H35. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hfc ]. % 8.61/8.85 apply (zenon_L55_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hfd ]. % 8.61/8.85 apply (zenon_L313_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_Hf6 | zenon_intro zenon_He5 ]. % 8.61/8.85 apply (zenon_L57_); trivial. % 8.61/8.85 apply (zenon_L267_); trivial. % 8.61/8.85 (* end of lemma zenon_L690_ *) % 8.61/8.85 assert (zenon_L691_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.61/8.85 do 0 intro. intros zenon_H105 zenon_Hd4 zenon_Hd0 zenon_H35 zenon_He8 zenon_He4 zenon_Hff zenon_H195. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H30 | zenon_intro zenon_H106 ]. % 8.61/8.85 apply (zenon_L66_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H107 ]. % 8.61/8.85 apply (zenon_L246_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hfe | zenon_intro zenon_H103 ]. % 8.61/8.85 apply (zenon_L679_); trivial. % 8.61/8.85 apply (zenon_L324_); trivial. % 8.61/8.85 (* end of lemma zenon_L691_ *) % 8.61/8.85 assert (zenon_L692_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e2)) -> False). % 8.61/8.85 do 0 intro. intros zenon_H331 zenon_H127 zenon_H274 zenon_Ha3 zenon_Hff zenon_He4 zenon_H35 zenon_Hd0 zenon_Hd4 zenon_H105 zenon_Ha8 zenon_He8. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H331); [ zenon_intro zenon_H103 | zenon_intro zenon_H332 ]. % 8.61/8.85 apply (zenon_L315_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H332); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H333 ]. % 8.61/8.85 apply (zenon_L124_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H333); [ zenon_intro zenon_H195 | zenon_intro zenon_H5a ]. % 8.61/8.85 apply (zenon_L691_); trivial. % 8.61/8.85 apply (zenon_L439_); trivial. % 8.61/8.85 (* end of lemma zenon_L692_ *) % 8.61/8.85 assert (zenon_L693_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> False). % 8.61/8.85 do 0 intro. intros zenon_H322 zenon_H16d zenon_H98 zenon_H6b zenon_H1dd zenon_H7d zenon_Hf9 zenon_H191 zenon_H169 zenon_H29f zenon_H7e zenon_H331 zenon_H127 zenon_H274 zenon_Ha3 zenon_Hff zenon_He4 zenon_H35 zenon_Hd0 zenon_Hd4 zenon_H105 zenon_Ha8. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H323 ]. % 8.61/8.85 apply (zenon_L690_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H324 ]. % 8.61/8.85 apply (zenon_L628_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_Hbd | zenon_intro zenon_He8 ]. % 8.61/8.85 apply (zenon_L398_); trivial. % 8.61/8.85 apply (zenon_L692_); trivial. % 8.61/8.85 (* end of lemma zenon_L693_ *) % 8.61/8.85 assert (zenon_L694_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> False). % 8.61/8.85 do 0 intro. intros zenon_H11f zenon_H31 zenon_H1e zenon_H67 zenon_H2c3 zenon_H2a3 zenon_H41 zenon_Hc2 zenon_H1df zenon_Hf0 zenon_H322 zenon_H16d zenon_H98 zenon_H6b zenon_H1dd zenon_H7d zenon_Hf9 zenon_H191 zenon_H169 zenon_H29f zenon_H7e zenon_H331 zenon_H127 zenon_H274 zenon_Ha3 zenon_Hff zenon_He4 zenon_H35 zenon_Hd0 zenon_H105 zenon_Ha8. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.61/8.85 apply (zenon_L4_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.61/8.85 apply (zenon_L263_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.61/8.85 apply (zenon_L689_); trivial. % 8.61/8.85 apply (zenon_L693_); trivial. % 8.61/8.85 (* end of lemma zenon_L694_ *) % 8.61/8.85 assert (zenon_L695_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> False). % 8.61/8.85 do 0 intro. intros zenon_H371 zenon_Hf0 zenon_H41 zenon_H2a3 zenon_H2c3 zenon_H67 zenon_H1e zenon_H31 zenon_H11f zenon_Hc2 zenon_H322 zenon_H16d zenon_H98 zenon_H6b zenon_H1dd zenon_H7d zenon_Hf9 zenon_H191 zenon_H169 zenon_H29f zenon_H7e zenon_H331 zenon_H127 zenon_H274 zenon_Ha3 zenon_Hff zenon_He4 zenon_H35 zenon_Hd0 zenon_H105 zenon_Ha8. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H371); [ zenon_intro zenon_H14e | zenon_intro zenon_H372 ]. % 8.61/8.85 apply (zenon_L94_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H372); [ zenon_intro zenon_H1df | zenon_intro zenon_H373 ]. % 8.61/8.85 apply (zenon_L694_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H373); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hd4 ]. % 8.61/8.85 apply (zenon_L42_); trivial. % 8.61/8.85 apply (zenon_L693_); trivial. % 8.61/8.85 (* end of lemma zenon_L695_ *) % 8.61/8.85 assert (zenon_L696_ : (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (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 (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.61/8.85 do 0 intro. intros zenon_Ha8 zenon_H105 zenon_Hd0 zenon_He4 zenon_Hff zenon_H274 zenon_H127 zenon_H331 zenon_H7e zenon_H29f zenon_H169 zenon_H191 zenon_Hf9 zenon_H7d zenon_H322 zenon_Hc2 zenon_H11f zenon_H31 zenon_H1e zenon_H67 zenon_H2c3 zenon_H2a3 zenon_H41 zenon_H371 zenon_H1dd zenon_H6b zenon_H98 zenon_Ha3 zenon_H16d zenon_H35. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hfc ]. % 8.61/8.85 apply (zenon_L695_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hfd ]. % 8.61/8.85 apply (zenon_L313_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_Hf6 | zenon_intro zenon_He5 ]. % 8.61/8.85 apply (zenon_L57_); trivial. % 8.61/8.85 apply (zenon_L267_); trivial. % 8.61/8.85 (* end of lemma zenon_L696_ *) % 8.61/8.85 assert (zenon_L697_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (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 (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.61/8.85 do 0 intro. intros zenon_H16d zenon_Ha3 zenon_H6b zenon_H1dd zenon_H371 zenon_H2a3 zenon_H2c3 zenon_H67 zenon_H1e zenon_H31 zenon_H11f zenon_Hc2 zenon_H322 zenon_H7d zenon_Hf9 zenon_H169 zenon_H29f zenon_H7e zenon_H331 zenon_H127 zenon_Hff zenon_He4 zenon_Hd0 zenon_H105 zenon_H35 zenon_H41 zenon_Ha8 zenon_H191 zenon_H1d9 zenon_H98. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2a3); [ zenon_intro zenon_H274 | zenon_intro zenon_H2b2 ]. % 8.61/8.85 apply (zenon_L696_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H2b3 ]. % 8.61/8.85 apply (zenon_L247_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H196 | zenon_intro zenon_H1b1 ]. % 8.61/8.85 apply (zenon_L327_); trivial. % 8.61/8.85 apply (zenon_L375_); trivial. % 8.61/8.85 (* end of lemma zenon_L697_ *) % 8.61/8.85 assert (zenon_L698_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.61/8.85 do 0 intro. intros zenon_Hbf zenon_Hfe zenon_H153 zenon_H154 zenon_H91 zenon_H7d zenon_Ha8 zenon_H98. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H7e | zenon_intro zenon_Hc0 ]. % 8.61/8.85 apply (zenon_L96_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H93 | zenon_intro zenon_Hc1 ]. % 8.61/8.85 apply (zenon_L97_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H3b | zenon_intro zenon_Hbd ]. % 8.61/8.85 apply (zenon_L396_); trivial. % 8.61/8.85 apply (zenon_L38_); trivial. % 8.61/8.85 (* end of lemma zenon_L698_ *) % 8.61/8.85 assert (zenon_L699_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.61/8.85 do 0 intro. intros zenon_H2a3 zenon_H127 zenon_H103 zenon_H35 zenon_H41 zenon_Ha8 zenon_H191 zenon_H1d9 zenon_H98. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2a3); [ zenon_intro zenon_H274 | zenon_intro zenon_H2b2 ]. % 8.61/8.85 apply (zenon_L315_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H2b3 ]. % 8.61/8.85 apply (zenon_L247_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H196 | zenon_intro zenon_H1b1 ]. % 8.61/8.85 apply (zenon_L327_); trivial. % 8.61/8.85 apply (zenon_L375_); trivial. % 8.61/8.85 (* end of lemma zenon_L699_ *) % 8.61/8.85 assert (zenon_L700_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> False). % 8.61/8.85 do 0 intro. intros zenon_H329 zenon_H91 zenon_H154 zenon_H153 zenon_Hbf zenon_H7d zenon_H197 zenon_H331 zenon_H98 zenon_H1d9 zenon_H191 zenon_H41 zenon_H127 zenon_H2a3 zenon_Ha3 zenon_Hff zenon_He4 zenon_H35 zenon_Hd0 zenon_H10f zenon_H105 zenon_Ha8. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hfe | zenon_intro zenon_H32a ]. % 8.61/8.85 apply (zenon_L698_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H108 | zenon_intro zenon_H32b ]. % 8.61/8.85 apply (zenon_L584_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H3c | zenon_intro zenon_He8 ]. % 8.61/8.85 apply (zenon_L191_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H331); [ zenon_intro zenon_H103 | zenon_intro zenon_H332 ]. % 8.61/8.85 apply (zenon_L699_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H332); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H333 ]. % 8.61/8.85 apply (zenon_L124_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H333); [ zenon_intro zenon_H195 | zenon_intro zenon_H5a ]. % 8.61/8.85 apply (zenon_L687_); trivial. % 8.61/8.85 apply (zenon_L439_); trivial. % 8.61/8.85 (* end of lemma zenon_L700_ *) % 8.61/8.85 assert (zenon_L701_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> False). % 8.61/8.85 do 0 intro. intros zenon_H329 zenon_H98 zenon_H91 zenon_H154 zenon_H153 zenon_Hbf zenon_H7d zenon_H191 zenon_H197 zenon_H331 zenon_H127 zenon_H274 zenon_Ha3 zenon_Hff zenon_He4 zenon_H35 zenon_Hd0 zenon_Hd4 zenon_H105 zenon_Ha8. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hfe | zenon_intro zenon_H32a ]. % 8.61/8.85 apply (zenon_L698_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H108 | zenon_intro zenon_H32b ]. % 8.61/8.85 apply (zenon_L584_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H3c | zenon_intro zenon_He8 ]. % 8.61/8.85 apply (zenon_L191_); trivial. % 8.61/8.85 apply (zenon_L692_); trivial. % 8.61/8.85 (* end of lemma zenon_L701_ *) % 8.61/8.85 assert (zenon_L702_ : (((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)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.61/8.85 do 0 intro. intros zenon_H303 zenon_H66 zenon_H137 zenon_Ha8 zenon_H105 zenon_Hd0 zenon_He4 zenon_Hff zenon_Ha3 zenon_H274 zenon_H127 zenon_H331 zenon_H197 zenon_H191 zenon_H7d zenon_Hbf zenon_H153 zenon_H154 zenon_H98 zenon_H329 zenon_H1d9 zenon_H41 zenon_H2a3 zenon_H67 zenon_H1e zenon_H31 zenon_H11f zenon_H109 zenon_H35. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.61/8.85 apply (zenon_L250_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.61/8.85 apply (zenon_L149_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.61/8.85 apply (zenon_L4_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.61/8.85 apply (zenon_L263_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.61/8.85 apply (zenon_L700_); trivial. % 8.61/8.85 apply (zenon_L701_); trivial. % 8.61/8.85 apply (zenon_L106_); trivial. % 8.61/8.85 (* end of lemma zenon_L702_ *) % 8.61/8.85 assert (zenon_L703_ : ((op (e0) (e0)) = (e0)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (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 (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.61/8.85 do 0 intro. intros zenon_H1e zenon_H93 zenon_H1d9 zenon_H173 zenon_H22d zenon_H1d7 zenon_Ha8 zenon_H192 zenon_H2b8 zenon_H67 zenon_H197 zenon_H2b zenon_Hab zenon_Hc2 zenon_H1f6 zenon_H78 zenon_H127 zenon_H31 zenon_H25 zenon_H22e zenon_H153 zenon_H170 zenon_Hc5 zenon_H3a zenon_H2a2 zenon_H29f zenon_H2d2 zenon_H2d4 zenon_H145 zenon_H10c zenon_Hb4 zenon_H32e zenon_H109 zenon_He7 zenon_Hff zenon_H2d8 zenon_H329 zenon_H2a5 zenon_H129 zenon_H12b zenon_H2fc zenon_H36 zenon_H11f zenon_H124 zenon_H2bf zenon_H2e2 zenon_H164 zenon_Hf8 zenon_H2a3 zenon_Hf3 zenon_H285 zenon_H2e8 zenon_H27f zenon_H137 zenon_H282 zenon_H150 zenon_H74 zenon_H6c zenon_Hb7 zenon_H2c9 zenon_H19a zenon_H295 zenon_H2a1 zenon_H1dc zenon_H169 zenon_H2c0 zenon_H2b5 zenon_H2a4 zenon_H270 zenon_H1f zenon_Hd0 zenon_H2f3 zenon_H2df zenon_H1d3 zenon_H105 zenon_H322 zenon_He4 zenon_Hbf zenon_H303 zenon_Hba zenon_H331 zenon_H11e zenon_Heb zenon_H94 zenon_H336 zenon_H134 zenon_H2f8 zenon_H300 zenon_H90 zenon_Hf9 zenon_H7d zenon_H1dd zenon_H6b zenon_H98 zenon_Ha3 zenon_H16d zenon_H35. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.61/8.85 apply (zenon_L21_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.61/8.85 apply (zenon_L34_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.61/8.85 apply (zenon_L495_); trivial. % 8.61/8.85 apply (zenon_L690_); trivial. % 8.61/8.85 (* end of lemma zenon_L703_ *) % 8.61/8.85 assert (zenon_L704_ : ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op 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(e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.61/8.85 do 0 intro. intros zenon_Hfe zenon_H35 zenon_H16d zenon_Ha3 zenon_H6b zenon_H1dd zenon_Hf9 zenon_H90 zenon_H300 zenon_H2f8 zenon_H134 zenon_H336 zenon_H94 zenon_Heb zenon_H11e zenon_H331 zenon_Hba zenon_H303 zenon_Hbf zenon_He4 zenon_H322 zenon_H105 zenon_H1d3 zenon_H2df zenon_H2f3 zenon_Hd0 zenon_H1f zenon_H270 zenon_H2a4 zenon_H2b5 zenon_H2c0 zenon_H169 zenon_H1dc zenon_H2a1 zenon_H295 zenon_H19a zenon_H2c9 zenon_Hb7 zenon_H6c zenon_H74 zenon_H150 zenon_H282 zenon_H137 zenon_H27f zenon_H2e8 zenon_H285 zenon_Hf3 zenon_H2a3 zenon_Hf8 zenon_H164 zenon_H2e2 zenon_H2bf zenon_H124 zenon_H11f zenon_H36 zenon_H2fc zenon_H12b zenon_H129 zenon_H2a5 zenon_H329 zenon_H2d8 zenon_Hff zenon_He7 zenon_H109 zenon_H32e zenon_Hb4 zenon_H10c zenon_H145 zenon_H2d4 zenon_H2d2 zenon_H29f zenon_H2a2 zenon_H3a zenon_Hc5 zenon_H170 zenon_H153 zenon_H22e zenon_H25 zenon_H31 zenon_H127 zenon_H78 zenon_H1f6 zenon_Hc2 zenon_Hab zenon_H2b zenon_H197 zenon_H67 zenon_H2b8 zenon_H192 zenon_H1d7 zenon_H22d zenon_H173 zenon_H1d9 zenon_H1e zenon_H91 zenon_H7d zenon_Ha8 zenon_H98. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H7e | zenon_intro zenon_Hc0 ]. % 8.61/8.85 apply (zenon_L96_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H93 | zenon_intro zenon_Hc1 ]. % 8.61/8.85 apply (zenon_L703_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H3b | zenon_intro zenon_Hbd ]. % 8.61/8.85 apply (zenon_L396_); trivial. % 8.61/8.85 apply (zenon_L38_); trivial. % 8.61/8.85 (* end of lemma zenon_L704_ *) % 8.61/8.85 assert (zenon_L705_ : ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (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 (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.61/8.85 do 0 intro. intros zenon_H191 zenon_H36a zenon_H9a zenon_Hed zenon_Hc9 zenon_Ha8 zenon_H7d zenon_H1e zenon_H1d9 zenon_H173 zenon_H22d zenon_H1d7 zenon_H192 zenon_H2b8 zenon_H67 zenon_H197 zenon_H2b zenon_Hab zenon_Hc2 zenon_H1f6 zenon_H78 zenon_H127 zenon_H31 zenon_H25 zenon_H22e zenon_H153 zenon_H170 zenon_Hc5 zenon_H3a zenon_H2a2 zenon_H29f zenon_H2d2 zenon_H2d4 zenon_H145 zenon_H10c zenon_Hb4 zenon_H32e zenon_H109 zenon_He7 zenon_Hff zenon_H2d8 zenon_H329 zenon_H2a5 zenon_H129 zenon_H12b zenon_H2fc zenon_H36 zenon_H11f zenon_H124 zenon_H2bf zenon_H2e2 zenon_H164 zenon_Hf8 zenon_H2a3 zenon_Hf3 zenon_H285 zenon_H2e8 zenon_H27f zenon_H137 zenon_H282 zenon_H150 zenon_H74 zenon_H6c zenon_Hb7 zenon_H2c9 zenon_H19a zenon_H295 zenon_H2a1 zenon_H1dc zenon_H169 zenon_H2c0 zenon_H2b5 zenon_H2a4 zenon_H270 zenon_H1f zenon_Hd0 zenon_H2f3 zenon_H2df zenon_H1d3 zenon_H105 zenon_H322 zenon_He4 zenon_Hbf zenon_H303 zenon_Hba zenon_H331 zenon_H11e zenon_Heb zenon_H94 zenon_H336 zenon_H134 zenon_H2f8 zenon_H300 zenon_H90 zenon_Hf9 zenon_H1dd zenon_H6b zenon_H16d zenon_H35 zenon_Hfe zenon_Ha3 zenon_H98. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.61/8.85 apply (zenon_L683_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.61/8.85 apply (zenon_L74_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.61/8.85 apply (zenon_L704_); trivial. % 8.61/8.85 apply (zenon_L57_); trivial. % 8.61/8.85 (* end of lemma zenon_L705_ *) % 8.61/8.85 assert (zenon_L706_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = 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(e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (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 (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.61/8.85 do 0 intro. intros zenon_Hed zenon_H9a zenon_H36a zenon_H191 zenon_H98 zenon_Ha8 zenon_H7d zenon_H1e zenon_H1d9 zenon_H173 zenon_H22d zenon_H1d7 zenon_H192 zenon_H2b8 zenon_H67 zenon_H197 zenon_H2b zenon_Hab zenon_Hc2 zenon_H1f6 zenon_H78 zenon_H127 zenon_H31 zenon_H25 zenon_H22e zenon_H153 zenon_H170 zenon_Hc5 zenon_H3a zenon_H2a2 zenon_H29f zenon_H2d2 zenon_H2d4 zenon_H145 zenon_H10c zenon_Hb4 zenon_H32e zenon_He7 zenon_Hff zenon_H2d8 zenon_H329 zenon_H2a5 zenon_H129 zenon_H12b zenon_H2fc zenon_H36 zenon_H11f zenon_H124 zenon_H2bf zenon_H2e2 zenon_H164 zenon_Hf8 zenon_H2a3 zenon_Hf3 zenon_H285 zenon_H2e8 zenon_H27f zenon_H137 zenon_H282 zenon_H150 zenon_H74 zenon_H6c zenon_Hb7 zenon_H2c9 zenon_H19a zenon_H295 zenon_H2a1 zenon_H1dc zenon_H169 zenon_H2c0 zenon_H2b5 zenon_H2a4 zenon_H270 zenon_H1f zenon_Hd0 zenon_H2f3 zenon_H2df zenon_H1d3 zenon_H105 zenon_H322 zenon_He4 zenon_Hbf zenon_H303 zenon_Hba zenon_H331 zenon_H11e zenon_Heb zenon_H94 zenon_H336 zenon_H134 zenon_H2f8 zenon_H300 zenon_H90 zenon_Hf9 zenon_H1dd zenon_H6b zenon_Ha3 zenon_H16d zenon_Hfe zenon_H109 zenon_H35. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.61/8.85 apply (zenon_L705_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.61/8.85 apply (zenon_L149_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.61/8.85 apply (zenon_L704_); trivial. % 8.61/8.85 apply (zenon_L106_); trivial. % 8.61/8.85 (* end of lemma zenon_L706_ *) % 8.61/8.85 assert (zenon_L707_ : (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((op (e1) (op (e1) (e3))) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (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 (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.61/8.85 do 0 intro. intros zenon_H41 zenon_H2c3 zenon_H371 zenon_Hed zenon_H9a zenon_H36a zenon_H191 zenon_H98 zenon_Ha8 zenon_H7d zenon_H1e zenon_H1d9 zenon_H173 zenon_H22d zenon_H1d7 zenon_H192 zenon_H2b8 zenon_H67 zenon_H197 zenon_H2b zenon_Hab zenon_Hc2 zenon_H1f6 zenon_H78 zenon_H127 zenon_H31 zenon_H25 zenon_H22e zenon_H153 zenon_H170 zenon_Hc5 zenon_H3a zenon_H2a2 zenon_H29f zenon_H2d2 zenon_H2d4 zenon_H145 zenon_H10c zenon_Hb4 zenon_H32e zenon_He7 zenon_Hff zenon_H2d8 zenon_H329 zenon_H2a5 zenon_H129 zenon_H12b zenon_H2fc zenon_H36 zenon_H11f zenon_H124 zenon_H2bf zenon_H2e2 zenon_H164 zenon_Hf8 zenon_H2a3 zenon_Hf3 zenon_H285 zenon_H2e8 zenon_H27f zenon_H137 zenon_H282 zenon_H150 zenon_H74 zenon_H6c zenon_Hb7 zenon_H2c9 zenon_H19a zenon_H295 zenon_H2a1 zenon_H1dc zenon_H169 zenon_H2c0 zenon_H2b5 zenon_H2a4 zenon_H270 zenon_H1f zenon_Hd0 zenon_H2f3 zenon_H2df zenon_H1d3 zenon_H105 zenon_H322 zenon_He4 zenon_Hbf zenon_H303 zenon_Hba zenon_H331 zenon_H11e zenon_Heb zenon_H94 zenon_H336 zenon_H134 zenon_H2f8 zenon_H300 zenon_H90 zenon_Hf9 zenon_H1dd zenon_H6b zenon_Ha3 zenon_H16d zenon_H109 zenon_H35. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.61/8.85 apply (zenon_L21_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.61/8.85 apply (zenon_L656_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.61/8.85 apply (zenon_L697_); trivial. % 8.61/8.85 apply (zenon_L706_); trivial. % 8.61/8.85 (* end of lemma zenon_L707_ *) % 8.61/8.85 assert (zenon_L708_ : (((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 (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.61/8.85 do 0 intro. intros zenon_H303 zenon_H66 zenon_H137 zenon_Hf4 zenon_H169 zenon_H98 zenon_Ha8 zenon_H7d zenon_H154 zenon_H153 zenon_Hfe zenon_Hbf zenon_H109 zenon_H35. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.61/8.85 apply (zenon_L250_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.61/8.85 apply (zenon_L103_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.61/8.85 apply (zenon_L698_); trivial. % 8.61/8.85 apply (zenon_L106_); trivial. % 8.61/8.85 (* end of lemma zenon_L708_ *) % 8.61/8.85 assert (zenon_L709_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.61/8.85 do 0 intro. intros zenon_H303 zenon_H1f6 zenon_H36a zenon_Ha3 zenon_H9a zenon_H11e zenon_H78 zenon_H1e zenon_H164 zenon_H134 zenon_Hed zenon_H16d zenon_He4 zenon_He7 zenon_H71 zenon_H191 zenon_H98 zenon_Ha8 zenon_H7d zenon_H154 zenon_H153 zenon_Hbf zenon_H109 zenon_H35. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.61/8.85 apply (zenon_L21_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.61/8.85 apply (zenon_L314_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.61/8.85 apply (zenon_L23_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.61/8.85 apply (zenon_L683_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.61/8.85 apply (zenon_L149_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.61/8.85 apply (zenon_L698_); trivial. % 8.61/8.85 apply (zenon_L106_); trivial. % 8.61/8.85 (* end of lemma zenon_L709_ *) % 8.61/8.85 assert (zenon_L710_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.61/8.85 do 0 intro. intros zenon_H322 zenon_H7d zenon_Hf0 zenon_H191 zenon_H169 zenon_Ha8 zenon_H59 zenon_H98. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H323 ]. % 8.61/8.85 apply (zenon_L55_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H324 ]. % 8.61/8.85 apply (zenon_L628_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_Hbd | zenon_intro zenon_He8 ]. % 8.61/8.85 apply (zenon_L38_); trivial. % 8.61/8.85 apply (zenon_L492_); trivial. % 8.61/8.85 (* end of lemma zenon_L710_ *) % 8.61/8.85 assert (zenon_L711_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (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) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.61/8.85 do 0 intro. intros zenon_H16d zenon_Ha3 zenon_H322 zenon_H7d zenon_H169 zenon_Ha8 zenon_Hf9 zenon_H303 zenon_H129 zenon_Hbf zenon_He7 zenon_He4 zenon_Hed zenon_H134 zenon_H164 zenon_H1e zenon_H78 zenon_H11e zenon_H9a zenon_H36a zenon_H1f6 zenon_H2df zenon_H109 zenon_H1dd zenon_H90 zenon_H300 zenon_H2f8 zenon_H336 zenon_H94 zenon_H331 zenon_Hba zenon_H105 zenon_H1d3 zenon_H2f3 zenon_H1f zenon_H270 zenon_H2a4 zenon_H2b5 zenon_H2c0 zenon_H1dc zenon_H2a1 zenon_H295 zenon_H19a zenon_H2c9 zenon_Hb7 zenon_H6c zenon_H74 zenon_H150 zenon_H282 zenon_H137 zenon_H27f zenon_H2e8 zenon_H285 zenon_Hf3 zenon_H2a3 zenon_Hf8 zenon_H2e2 zenon_H2bf zenon_H124 zenon_H11f zenon_H36 zenon_H2fc zenon_H12b zenon_H2a5 zenon_H329 zenon_H2d8 zenon_Hff zenon_H32e zenon_Hb4 zenon_H10c zenon_H145 zenon_H2d4 zenon_H2d2 zenon_H29f zenon_H2a2 zenon_H3a zenon_Hc5 zenon_H170 zenon_H22e zenon_H25 zenon_H31 zenon_H127 zenon_Hc2 zenon_Hab zenon_H2b zenon_H67 zenon_H2b8 zenon_H192 zenon_H1d7 zenon_H22d zenon_H173 zenon_H1d9 zenon_H371 zenon_H153 zenon_Hd0 zenon_H35e zenon_H35d zenon_H34d zenon_H191 zenon_H197 zenon_Heb zenon_H98. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.61/8.85 apply (zenon_L4_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.61/8.85 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.61/8.85 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 8.61/8.85 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H118. zenon_intro zenon_H18a. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.61/8.85 apply (zenon_L21_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.61/8.85 apply (zenon_L314_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.61/8.85 apply (zenon_L70_); trivial. % 8.61/8.85 apply (zenon_L678_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.61/8.85 apply (zenon_L527_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.61/8.85 apply (zenon_L19_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.61/8.85 apply (zenon_L637_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.61/8.85 apply (zenon_L683_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.61/8.85 apply (zenon_L21_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.61/8.85 apply (zenon_L527_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.61/8.85 apply (zenon_L5_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.61/8.85 apply (zenon_L149_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.61/8.85 apply (zenon_L683_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.61/8.85 apply (zenon_L103_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.61/8.85 apply (zenon_L684_); trivial. % 8.61/8.85 apply (zenon_L106_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.61/8.85 apply (zenon_L125_); trivial. % 8.61/8.85 apply (zenon_L55_); trivial. % 8.61/8.85 apply (zenon_L246_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.61/8.85 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 8.61/8.85 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H41. zenon_intro zenon_H4a. % 8.61/8.85 apply (zenon_and_s _ _ zenon_H4a). zenon_intro zenon_H154. zenon_intro zenon_H2c3. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.61/8.85 apply (zenon_L21_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.61/8.85 apply (zenon_L314_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.61/8.85 apply (zenon_L697_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.61/8.85 apply (zenon_L5_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.61/8.85 apply (zenon_L149_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2a3); [ zenon_intro zenon_H274 | zenon_intro zenon_H2b2 ]. % 8.61/8.85 apply (zenon_L702_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H2b3 ]. % 8.61/8.85 apply (zenon_L247_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H196 | zenon_intro zenon_H1b1 ]. % 8.61/8.85 apply (zenon_L258_); trivial. % 8.61/8.85 apply (zenon_L553_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.61/8.85 apply (zenon_L509_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.61/8.85 apply (zenon_L97_); trivial. % 8.61/8.85 apply (zenon_L584_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.61/8.85 apply (zenon_L707_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.61/8.85 apply (zenon_L5_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.61/8.85 apply (zenon_L149_); trivial. % 8.61/8.85 apply (zenon_L708_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.61/8.85 apply (zenon_L707_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.61/8.85 apply (zenon_L709_); trivial. % 8.61/8.85 apply (zenon_L246_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.61/8.85 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 8.61/8.85 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 8.61/8.85 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H4c. zenon_intro zenon_H57. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.61/8.85 apply (zenon_L683_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.61/8.85 apply (zenon_L74_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.61/8.85 apply (zenon_L329_); trivial. % 8.61/8.85 apply (zenon_L57_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.61/8.85 apply (zenon_L99_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.61/8.85 apply (zenon_L329_); trivial. % 8.61/8.85 apply (zenon_L106_); trivial. % 8.61/8.85 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 8.61/8.85 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 8.61/8.85 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H59. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hfc ]. % 8.61/8.85 apply (zenon_L710_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hfd ]. % 8.61/8.85 apply (zenon_L265_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_Hf6 | zenon_intro zenon_He5 ]. % 8.61/8.85 apply (zenon_L57_); trivial. % 8.61/8.85 apply (zenon_L267_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.61/8.85 apply (zenon_L191_); trivial. % 8.61/8.85 apply (zenon_L53_); trivial. % 8.61/8.85 (* end of lemma zenon_L711_ *) % 8.61/8.85 assert (zenon_L712_ : ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((e2) = (op (op (e1) (e1)) (e1)))) -> False). % 8.61/8.85 do 0 intro. intros zenon_Hcb zenon_H358 zenon_H382. % 8.61/8.85 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H33d | zenon_intro zenon_H33e ]. % 8.61/8.85 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e2) = (op (op (e1) (e1)) (e1)))). % 8.61/8.85 intro zenon_D_pnotp. % 8.61/8.85 apply zenon_H382. % 8.61/8.85 rewrite <- zenon_D_pnotp. % 8.61/8.85 exact zenon_H33d. % 8.61/8.85 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H33e]. % 8.61/8.85 cut (((op (op (e1) (e1)) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H383]. % 8.61/8.85 congruence. % 8.61/8.85 cut (((op (e0) (e1)) = (e2)) = ((op (op (e1) (e1)) (e1)) = (e2))). % 8.61/8.85 intro zenon_D_pnotp. % 8.61/8.85 apply zenon_H383. % 8.61/8.85 rewrite <- zenon_D_pnotp. % 8.61/8.85 exact zenon_Hcb. % 8.61/8.85 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.61/8.85 cut (((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H375]. % 8.61/8.85 congruence. % 8.61/8.85 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H33d | zenon_intro zenon_H33e ]. % 8.61/8.85 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))). % 8.61/8.85 intro zenon_D_pnotp. % 8.61/8.85 apply zenon_H375. % 8.61/8.85 rewrite <- zenon_D_pnotp. % 8.61/8.85 exact zenon_H33d. % 8.61/8.85 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H33e]. % 8.61/8.85 cut (((op (op (e1) (e1)) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H374]. % 8.61/8.85 congruence. % 8.61/8.85 apply (zenon_L658_); trivial. % 8.61/8.85 apply zenon_H33e. apply refl_equal. % 8.61/8.85 apply zenon_H33e. apply refl_equal. % 8.61/8.85 apply zenon_H4b. apply refl_equal. % 8.61/8.85 apply zenon_H33e. apply refl_equal. % 8.61/8.85 apply zenon_H33e. apply refl_equal. % 8.61/8.85 (* end of lemma zenon_L712_ *) % 8.61/8.85 assert (zenon_L713_ : ((op (e2) (e0)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 8.61/8.85 do 0 intro. intros zenon_H27e zenon_Hcb zenon_H358. % 8.61/8.85 apply (zenon_notand_s _ _ ax7); [ zenon_intro zenon_H377 | zenon_intro zenon_H384 ]. % 8.61/8.85 apply zenon_H377. apply sym_equal. exact zenon_H358. % 8.61/8.85 apply (zenon_notand_s _ _ zenon_H384); [ zenon_intro zenon_H385 | zenon_intro zenon_H382 ]. % 8.61/8.85 elim (classic ((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H343 | zenon_intro zenon_H344 ]. % 8.61/8.85 cut (((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1)))) = ((e3) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))). % 8.61/8.85 intro zenon_D_pnotp. % 8.61/8.85 apply zenon_H385. % 8.61/8.85 rewrite <- zenon_D_pnotp. % 8.61/8.85 exact zenon_H343. % 8.61/8.85 cut (((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H344]. % 8.61/8.85 cut (((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H386]. % 8.61/8.85 congruence. % 8.61/8.85 cut (((op (e2) (e0)) = (e3)) = ((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (e3))). % 8.61/8.85 intro zenon_D_pnotp. % 8.61/8.85 apply zenon_H386. % 8.61/8.85 rewrite <- zenon_D_pnotp. % 8.61/8.85 exact zenon_H27e. % 8.61/8.85 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.61/8.85 cut (((op (e2) (e0)) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H387]. % 8.61/8.85 congruence. % 8.61/8.85 elim (classic ((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H343 | zenon_intro zenon_H344 ]. % 8.61/8.85 cut (((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1)))) = ((op (e2) (e0)) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))). % 8.61/8.85 intro zenon_D_pnotp. % 8.61/8.85 apply zenon_H387. % 8.61/8.85 rewrite <- zenon_D_pnotp. % 8.61/8.85 exact zenon_H343. % 8.61/8.85 cut (((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (op (op (e1) (e1)) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H344]. % 8.61/8.85 cut (((op (op (op (e1) (e1)) (e1)) (op (e1) (e1))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H388]. % 8.61/8.85 congruence. % 8.61/8.85 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H35b]. % 8.61/8.85 cut (((op (op (e1) (e1)) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H383]. % 8.61/8.85 congruence. % 8.61/8.85 cut (((op (e0) (e1)) = (e2)) = ((op (op (e1) (e1)) (e1)) = (e2))). % 8.61/8.85 intro zenon_D_pnotp. % 8.61/8.85 apply zenon_H383. % 8.61/8.85 rewrite <- zenon_D_pnotp. % 8.61/8.85 exact zenon_Hcb. % 8.61/8.85 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 8.61/8.85 cut (((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H375]. % 8.61/8.85 congruence. % 8.61/8.85 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H33d | zenon_intro zenon_H33e ]. % 8.61/8.85 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))). % 8.61/8.85 intro zenon_D_pnotp. % 8.61/8.85 apply zenon_H375. % 8.61/8.85 rewrite <- zenon_D_pnotp. % 8.61/8.85 exact zenon_H33d. % 8.61/8.85 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H33e]. % 8.61/8.85 cut (((op (op (e1) (e1)) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H374]. % 8.61/8.85 congruence. % 8.61/8.85 apply (zenon_L658_); trivial. % 8.61/8.85 apply zenon_H33e. apply refl_equal. % 8.61/8.85 apply zenon_H33e. apply refl_equal. % 8.61/8.85 apply zenon_H4b. apply refl_equal. % 8.61/8.85 exact (zenon_H35b zenon_H358). % 8.61/8.85 apply zenon_H344. apply refl_equal. % 8.61/8.85 apply zenon_H344. apply refl_equal. % 8.61/8.85 apply zenon_H58. apply refl_equal. % 8.61/8.85 apply zenon_H344. apply refl_equal. % 8.61/8.85 apply zenon_H344. apply refl_equal. % 8.61/8.85 apply (zenon_L712_); trivial. % 8.61/8.85 (* end of lemma zenon_L713_ *) % 8.61/8.85 assert (zenon_L714_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 8.61/8.85 do 0 intro. intros zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H15a zenon_Hcc zenon_H6c zenon_H1b1 zenon_H1dd. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H1d | zenon_intro zenon_H2e3 ]. % 8.61/8.85 apply (zenon_L1_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H6b | zenon_intro zenon_H2e4 ]. % 8.61/8.85 apply (zenon_L534_); trivial. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_Hcb | zenon_intro zenon_H274 ]. % 8.61/8.85 apply (zenon_L45_); trivial. % 8.61/8.85 apply (zenon_L557_); trivial. % 8.61/8.85 (* end of lemma zenon_L714_ *) % 8.61/8.85 assert (zenon_L715_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 8.61/8.85 do 0 intro. intros zenon_H389 zenon_Hcb zenon_H27e zenon_H2c9 zenon_H1dd zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H1b1 zenon_Hf3. % 8.61/8.85 apply (zenon_or_s _ _ zenon_H389); [ zenon_intro zenon_H358 | zenon_intro zenon_H38a ]. % 8.71/8.86 apply (zenon_L713_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H38a); [ zenon_intro zenon_H2a | zenon_intro zenon_H38b ]. % 8.71/8.86 apply (zenon_L307_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H38b); [ zenon_intro zenon_Hcc | zenon_intro zenon_Ha2 ]. % 8.71/8.86 apply (zenon_L714_); trivial. % 8.71/8.86 apply (zenon_L559_); trivial. % 8.71/8.86 (* end of lemma zenon_L715_ *) % 8.71/8.86 assert (zenon_L716_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 8.71/8.86 do 0 intro. intros zenon_H282 zenon_H137 zenon_H192 zenon_H145 zenon_Hb0 zenon_H389 zenon_Hcb zenon_H2c9 zenon_H1dd zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H1b1 zenon_Hf3. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H143 | zenon_intro zenon_H283 ]. % 8.71/8.86 apply (zenon_L673_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H284 ]. % 8.71/8.86 apply (zenon_L157_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H27e ]. % 8.71/8.86 apply (zenon_L84_); trivial. % 8.71/8.86 apply (zenon_L715_); trivial. % 8.71/8.86 (* end of lemma zenon_L716_ *) % 8.71/8.86 assert (zenon_L717_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 8.71/8.86 do 0 intro. intros zenon_H10c zenon_Hf3 zenon_H1b1 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H15a zenon_H1dd zenon_H2c9 zenon_H389 zenon_H145 zenon_H192 zenon_H137 zenon_H282 zenon_Hcb zenon_H6c zenon_H7d zenon_H29 zenon_H3c zenon_H109. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.71/8.86 apply (zenon_L716_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.71/8.86 apply (zenon_L45_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.71/8.86 apply (zenon_L161_); trivial. % 8.71/8.86 apply (zenon_L63_); trivial. % 8.71/8.86 (* end of lemma zenon_L717_ *) % 8.71/8.86 assert (zenon_L718_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((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 (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (op (e0) (e2))) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.71/8.86 do 0 intro. intros zenon_H11e zenon_H78 zenon_H109 zenon_H29 zenon_H7d zenon_H6c zenon_H282 zenon_H137 zenon_H192 zenon_H145 zenon_H389 zenon_H2c9 zenon_H1dd zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H1b1 zenon_Hf3 zenon_H10c zenon_H118 zenon_H3c zenon_Hff. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.71/8.86 apply (zenon_L21_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.71/8.86 apply (zenon_L717_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.71/8.86 apply (zenon_L70_); trivial. % 8.71/8.86 apply (zenon_L59_); trivial. % 8.71/8.86 (* end of lemma zenon_L718_ *) % 8.71/8.86 assert (zenon_L719_ : (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> False). % 8.71/8.86 do 0 intro. intros zenon_Ha8 zenon_H1b1 zenon_H1d8. % 8.71/8.86 cut (((op (e3) (e1)) = (e3)) = ((e2) = (e3))). % 8.71/8.86 intro zenon_D_pnotp. % 8.71/8.86 apply zenon_Ha8. % 8.71/8.86 rewrite <- zenon_D_pnotp. % 8.71/8.86 exact zenon_H1b1. % 8.71/8.86 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.71/8.86 cut (((op (e3) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H38c]. % 8.71/8.86 congruence. % 8.71/8.86 exact (zenon_H38c zenon_H1d8). % 8.71/8.86 apply zenon_H58. apply refl_equal. % 8.71/8.86 (* end of lemma zenon_L719_ *) % 8.71/8.86 assert (zenon_L720_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.71/8.86 do 0 intro. intros zenon_H2c0 zenon_H7d zenon_H6b zenon_H29 zenon_H41 zenon_H3c zenon_H197 zenon_Ha8 zenon_H1b1. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_Hcb | zenon_intro zenon_H2c4 ]. % 8.71/8.86 apply (zenon_L656_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H2c5 ]. % 8.71/8.86 apply (zenon_L85_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1d8 ]. % 8.71/8.86 apply (zenon_L191_); trivial. % 8.71/8.86 apply (zenon_L719_); trivial. % 8.71/8.86 (* end of lemma zenon_L720_ *) % 8.71/8.86 assert (zenon_L721_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (op (e2) (e2))) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 8.71/8.86 do 0 intro. intros zenon_H36a zenon_Ha3 zenon_Hc9 zenon_H169 zenon_H1b1 zenon_H4c zenon_H3c zenon_Ha8. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.71/8.86 apply (zenon_L674_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.71/8.86 apply (zenon_L432_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.71/8.86 apply (zenon_L342_); trivial. % 8.71/8.86 apply (zenon_L368_); trivial. % 8.71/8.86 (* end of lemma zenon_L721_ *) % 8.71/8.86 assert (zenon_L722_ : (((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)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> False). % 8.71/8.86 do 0 intro. intros zenon_H322 zenon_H7d zenon_Hf0 zenon_H1b1 zenon_Ha8 zenon_H65 zenon_He7 zenon_H3c. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H323 ]. % 8.71/8.86 apply (zenon_L55_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H324 ]. % 8.71/8.86 apply (zenon_L719_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_Hbd | zenon_intro zenon_He8 ]. % 8.71/8.86 apply (zenon_L295_); trivial. % 8.71/8.86 apply (zenon_L52_); trivial. % 8.71/8.86 (* end of lemma zenon_L722_ *) % 8.71/8.86 assert (zenon_L723_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.71/8.86 do 0 intro. intros zenon_Hf9 zenon_H3c zenon_He7 zenon_H65 zenon_Ha8 zenon_H7d zenon_H322 zenon_Ha3 zenon_H29 zenon_H2d2 zenon_H59 zenon_H1b1. % 8.71/8.86 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hfc ]. % 8.71/8.86 apply (zenon_L722_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hfd ]. % 8.71/8.86 apply (zenon_L553_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_Hf6 | zenon_intro zenon_He5 ]. % 8.71/8.86 apply (zenon_L466_); trivial. % 8.71/8.86 apply (zenon_L479_); trivial. % 8.71/8.86 (* end of lemma zenon_L723_ *) % 8.71/8.86 assert (zenon_L724_ : (((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 (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.71/8.86 do 0 intro. intros zenon_H303 zenon_H66 zenon_H137 zenon_H1dd zenon_H1b1 zenon_H6c zenon_Hcc zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H3b zenon_H7d zenon_H109 zenon_H35. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.71/8.86 apply (zenon_L250_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.71/8.86 apply (zenon_L714_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.71/8.86 apply (zenon_L396_); trivial. % 8.71/8.86 apply (zenon_L106_); trivial. % 8.71/8.86 (* end of lemma zenon_L724_ *) % 8.71/8.86 assert (zenon_L725_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((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 (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.71/8.86 do 0 intro. intros zenon_H2c0 zenon_H6b zenon_H35 zenon_H109 zenon_H7d zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H6c zenon_H1dd zenon_H137 zenon_H66 zenon_H303 zenon_H3b zenon_H1f6 zenon_Ha8 zenon_H1b1. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_Hcb | zenon_intro zenon_H2c4 ]. % 8.71/8.86 apply (zenon_L656_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H2c5 ]. % 8.71/8.86 apply (zenon_L724_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1d8 ]. % 8.71/8.86 apply (zenon_L198_); trivial. % 8.71/8.86 apply (zenon_L719_); trivial. % 8.71/8.86 (* end of lemma zenon_L725_ *) % 8.71/8.86 assert (zenon_L726_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 8.71/8.86 do 0 intro. intros zenon_H282 zenon_H10f zenon_H12b zenon_He7 zenon_H195 zenon_He4 zenon_Hfe zenon_H16d zenon_H35 zenon_Hed zenon_Hf1 zenon_H27f zenon_Hcb zenon_H358. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H143 | zenon_intro zenon_H283 ]. % 8.71/8.86 apply (zenon_L253_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H284 ]. % 8.71/8.86 apply (zenon_L680_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H27e ]. % 8.71/8.86 apply (zenon_L435_); trivial. % 8.71/8.86 apply (zenon_L713_); trivial. % 8.71/8.86 (* end of lemma zenon_L726_ *) % 8.71/8.86 assert (zenon_L727_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.71/8.86 do 0 intro. intros zenon_H329 zenon_H358 zenon_Hcb zenon_H27f zenon_Hf1 zenon_Hed zenon_H16d zenon_He7 zenon_H12b zenon_H282 zenon_H7d zenon_Ha8 zenon_H105 zenon_H10f zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff zenon_H195. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hfe | zenon_intro zenon_H32a ]. % 8.71/8.86 apply (zenon_L726_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H108 | zenon_intro zenon_H32b ]. % 8.71/8.86 apply (zenon_L584_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H3c | zenon_intro zenon_He8 ]. % 8.71/8.86 apply (zenon_L368_); trivial. % 8.71/8.86 apply (zenon_L687_); trivial. % 8.71/8.86 (* end of lemma zenon_L727_ *) % 8.71/8.86 assert (zenon_L728_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.71/8.86 do 0 intro. intros zenon_H322 zenon_Ha8 zenon_H7d zenon_H282 zenon_H12b zenon_He7 zenon_H16d zenon_Hed zenon_H27f zenon_Hcb zenon_H358 zenon_H329 zenon_H66 zenon_H87 zenon_H3b zenon_H9a zenon_H105 zenon_H10f zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff zenon_H195. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H323 ]. % 8.71/8.86 apply (zenon_L727_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H324 ]. % 8.71/8.86 apply (zenon_L437_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_Hbd | zenon_intro zenon_He8 ]. % 8.71/8.86 apply (zenon_L513_); trivial. % 8.71/8.86 apply (zenon_L687_); trivial. % 8.71/8.86 (* end of lemma zenon_L728_ *) % 8.71/8.86 assert (zenon_L729_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 8.71/8.86 do 0 intro. intros zenon_H282 zenon_H165 zenon_H192 zenon_Hd4 zenon_Hfe zenon_H145 zenon_Hb0 zenon_H389 zenon_Hcb zenon_H2c9 zenon_H1dd zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H1b1 zenon_Hf3. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H143 | zenon_intro zenon_H283 ]. % 8.71/8.86 apply (zenon_L249_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H284 ]. % 8.71/8.86 apply (zenon_L68_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H27e ]. % 8.71/8.86 apply (zenon_L84_); trivial. % 8.71/8.86 apply (zenon_L715_); trivial. % 8.71/8.86 (* end of lemma zenon_L729_ *) % 8.71/8.86 assert (zenon_L730_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.71/8.86 do 0 intro. intros zenon_H329 zenon_Hf3 zenon_H1b1 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H15a zenon_H6c zenon_H1dd zenon_H2c9 zenon_Hcb zenon_H389 zenon_Hb0 zenon_H145 zenon_H192 zenon_H165 zenon_H282 zenon_H7d zenon_Ha8 zenon_H105 zenon_Hd4 zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff zenon_H195. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hfe | zenon_intro zenon_H32a ]. % 8.71/8.86 apply (zenon_L729_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H108 | zenon_intro zenon_H32b ]. % 8.71/8.86 apply (zenon_L584_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H3c | zenon_intro zenon_He8 ]. % 8.71/8.86 apply (zenon_L368_); trivial. % 8.71/8.86 apply (zenon_L691_); trivial. % 8.71/8.86 (* end of lemma zenon_L730_ *) % 8.71/8.86 assert (zenon_L731_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.71/8.86 do 0 intro. intros zenon_H36a zenon_Hf3 zenon_H1b1 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H6c zenon_H1dd zenon_H2c9 zenon_H389 zenon_Ha3 zenon_H15a zenon_H322 zenon_Ha8 zenon_H7d zenon_H282 zenon_H12b zenon_He7 zenon_H16d zenon_Hed zenon_H27f zenon_Hcb zenon_H358 zenon_H329 zenon_H66 zenon_H87 zenon_H3b zenon_H9a zenon_H105 zenon_H10f zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.71/8.86 apply (zenon_L715_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.71/8.86 apply (zenon_L395_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.71/8.86 apply (zenon_L346_); trivial. % 8.71/8.86 apply (zenon_L728_); trivial. % 8.71/8.86 (* end of lemma zenon_L731_ *) % 8.71/8.86 assert (zenon_L732_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.71/8.86 do 0 intro. intros zenon_H285 zenon_H137 zenon_H192 zenon_H145 zenon_Hb0 zenon_H67 zenon_H31 zenon_H11f zenon_H78 zenon_H36a zenon_Hf3 zenon_H1b1 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H6c zenon_H1dd zenon_H2c9 zenon_H389 zenon_Ha3 zenon_H15a zenon_H322 zenon_Ha8 zenon_H7d zenon_H282 zenon_H12b zenon_He7 zenon_H16d zenon_Hed zenon_H27f zenon_Hcb zenon_H358 zenon_H329 zenon_H66 zenon_H87 zenon_H3b zenon_H9a zenon_H105 zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H143 | zenon_intro zenon_H286 ]. % 8.71/8.86 apply (zenon_L673_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H165 | zenon_intro zenon_H287 ]. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.71/8.86 apply (zenon_L715_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.71/8.86 apply (zenon_L395_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.71/8.86 apply (zenon_L346_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.71/8.86 apply (zenon_L4_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.71/8.86 apply (zenon_L263_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.71/8.86 apply (zenon_L728_); trivial. % 8.71/8.86 apply (zenon_L730_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H80 | zenon_intro zenon_H10f ]. % 8.71/8.86 apply (zenon_L40_); trivial. % 8.71/8.86 apply (zenon_L731_); trivial. % 8.71/8.86 (* end of lemma zenon_L732_ *) % 8.71/8.86 assert (zenon_L733_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 8.71/8.86 do 0 intro. intros zenon_H29 zenon_Ha7 zenon_Ha3. % 8.71/8.86 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H58 ]. % 8.71/8.86 cut (((e3) = (e3)) = ((e1) = (e3))). % 8.71/8.86 intro zenon_D_pnotp. % 8.71/8.86 apply zenon_Ha3. % 8.71/8.86 rewrite <- zenon_D_pnotp. % 8.71/8.86 exact zenon_Ha4. % 8.71/8.86 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 8.71/8.86 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 8.71/8.86 congruence. % 8.71/8.86 cut (((op (e1) (e2)) = (e1)) = ((e3) = (e1))). % 8.71/8.86 intro zenon_D_pnotp. % 8.71/8.86 apply zenon_Ha5. % 8.71/8.86 rewrite <- zenon_D_pnotp. % 8.71/8.86 exact zenon_H29. % 8.71/8.86 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 8.71/8.86 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 8.71/8.86 congruence. % 8.71/8.86 exact (zenon_Haa zenon_Ha7). % 8.71/8.86 apply zenon_H40. apply refl_equal. % 8.71/8.86 apply zenon_H58. apply refl_equal. % 8.71/8.86 apply zenon_H58. apply refl_equal. % 8.71/8.86 (* end of lemma zenon_L733_ *) % 8.71/8.86 assert (zenon_L734_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (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). % 8.71/8.86 do 0 intro. intros zenon_H300 zenon_H25 zenon_H1e zenon_Hf6 zenon_H29f zenon_H90 zenon_H3b zenon_H134 zenon_Ha7. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H24 | zenon_intro zenon_H301 ]. % 8.71/8.86 apply (zenon_L2_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H301); [ zenon_intro zenon_H71 | zenon_intro zenon_H302 ]. % 8.71/8.86 apply (zenon_L266_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H7e | zenon_intro zenon_H276 ]. % 8.71/8.86 apply (zenon_L565_); trivial. % 8.71/8.86 apply (zenon_L560_); trivial. % 8.71/8.86 (* end of lemma zenon_L734_ *) % 8.71/8.86 assert (zenon_L735_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((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). % 8.71/8.86 do 0 intro. intros zenon_H2df zenon_H66 zenon_Ha3 zenon_H7d zenon_H300 zenon_H25 zenon_H1e zenon_H29f zenon_H90 zenon_H3b zenon_H134 zenon_Ha7. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.71/8.86 apply (zenon_L19_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.71/8.86 apply (zenon_L733_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.71/8.86 apply (zenon_L396_); trivial. % 8.71/8.86 apply (zenon_L734_); trivial. % 8.71/8.86 (* end of lemma zenon_L735_ *) % 8.71/8.86 assert (zenon_L736_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (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 (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (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)) = (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) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 8.71/8.86 do 0 intro. intros zenon_Hba zenon_Hff zenon_He4 zenon_Hd0 zenon_H105 zenon_H9a zenon_H329 zenon_H358 zenon_Hcb zenon_H27f zenon_Hed zenon_H16d zenon_He7 zenon_H12b zenon_H282 zenon_Ha8 zenon_H322 zenon_H15a zenon_H389 zenon_H2c9 zenon_H1dd zenon_H6c zenon_H164 zenon_H1f zenon_H2e2 zenon_H36a zenon_H78 zenon_H11f zenon_H31 zenon_H67 zenon_Hb0 zenon_H145 zenon_H192 zenon_H137 zenon_H285 zenon_Hf3 zenon_H1b1 zenon_H134 zenon_H3b zenon_H90 zenon_H29f zenon_H1e zenon_H25 zenon_H300 zenon_H7d zenon_H66 zenon_H2df zenon_H35 zenon_Ha3. % 8.71/8.86 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H87 | zenon_intro zenon_Hbb ]. % 8.71/8.86 apply (zenon_L732_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hbc ]. % 8.71/8.86 apply (zenon_L559_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hb3 ]. % 8.71/8.86 apply (zenon_L735_); trivial. % 8.71/8.86 apply (zenon_L124_); trivial. % 8.71/8.86 (* end of lemma zenon_L736_ *) % 8.71/8.86 assert (zenon_L737_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.71/8.86 do 0 intro. intros zenon_H336 zenon_H1f6 zenon_H303 zenon_H109 zenon_H2c0 zenon_H36 zenon_H35 zenon_H2df zenon_H66 zenon_H7d zenon_H300 zenon_H25 zenon_H1e zenon_H29f zenon_H90 zenon_H3b zenon_H134 zenon_Hf3 zenon_H285 zenon_H137 zenon_H192 zenon_H145 zenon_Hb0 zenon_H67 zenon_H31 zenon_H11f zenon_H78 zenon_H36a zenon_H2e2 zenon_H1f zenon_H164 zenon_H6c zenon_H1dd zenon_H2c9 zenon_H389 zenon_H322 zenon_Ha8 zenon_H282 zenon_H12b zenon_He7 zenon_H16d zenon_Hed zenon_H27f zenon_Hcb zenon_H358 zenon_H329 zenon_H9a zenon_H105 zenon_Hd0 zenon_He4 zenon_Hff zenon_Hba zenon_Ha3 zenon_H1b1. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.71/8.86 apply (zenon_L725_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.71/8.86 apply (zenon_L5_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.71/8.86 apply (zenon_L736_); trivial. % 8.71/8.86 apply (zenon_L553_); trivial. % 8.71/8.86 (* end of lemma zenon_L737_ *) % 8.71/8.86 assert (zenon_L738_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((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 (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.71/8.86 do 0 intro. intros zenon_H2c0 zenon_H6b zenon_H35 zenon_H109 zenon_H7d zenon_H3b zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H6c zenon_H1dd zenon_H137 zenon_H66 zenon_H303 zenon_H165 zenon_H78 zenon_Ha8 zenon_H1b1. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_Hcb | zenon_intro zenon_H2c4 ]. % 8.71/8.86 apply (zenon_L656_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H2c5 ]. % 8.71/8.86 apply (zenon_L724_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1d8 ]. % 8.71/8.86 apply (zenon_L626_); trivial. % 8.71/8.86 apply (zenon_L719_); trivial. % 8.71/8.86 (* end of lemma zenon_L738_ *) % 8.71/8.86 assert (zenon_L739_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.71/8.86 do 0 intro. intros zenon_H2c0 zenon_Hf3 zenon_H2c9 zenon_H27e zenon_H389 zenon_H1dd zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H165 zenon_H78 zenon_Ha8 zenon_H1b1. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_Hcb | zenon_intro zenon_H2c4 ]. % 8.71/8.86 apply (zenon_L715_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H2c5 ]. % 8.71/8.86 apply (zenon_L714_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1d8 ]. % 8.71/8.86 apply (zenon_L626_); trivial. % 8.71/8.86 apply (zenon_L719_); trivial. % 8.71/8.86 (* end of lemma zenon_L739_ *) % 8.71/8.86 assert (zenon_L740_ : (((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)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.71/8.86 do 0 intro. intros zenon_H303 zenon_Ha3 zenon_H27e zenon_H164 zenon_H6b zenon_H3b zenon_H7d zenon_H109 zenon_H35. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.71/8.86 apply (zenon_L674_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.71/8.86 apply (zenon_L534_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.71/8.86 apply (zenon_L396_); trivial. % 8.71/8.86 apply (zenon_L106_); trivial. % 8.71/8.86 (* end of lemma zenon_L740_ *) % 8.71/8.86 assert (zenon_L741_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (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 (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.71/8.86 do 0 intro. intros zenon_H336 zenon_H109 zenon_H303 zenon_H36 zenon_H35 zenon_H1b1 zenon_Ha8 zenon_H78 zenon_H165 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H6c zenon_H1dd zenon_H389 zenon_H27e zenon_H2c9 zenon_Hf3 zenon_H2c0 zenon_H2df zenon_Ha3 zenon_H276 zenon_Had zenon_H67 zenon_H3b zenon_H7d zenon_H1d9. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.71/8.86 apply (zenon_L740_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.71/8.86 apply (zenon_L5_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.71/8.86 apply (zenon_L739_); trivial. % 8.71/8.86 apply (zenon_L616_); trivial. % 8.71/8.86 (* end of lemma zenon_L741_ *) % 8.71/8.86 assert (zenon_L742_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (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)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (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 (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 8.71/8.86 do 0 intro. intros zenon_H36a zenon_H1d9 zenon_H7d zenon_H67 zenon_Had zenon_H276 zenon_Ha3 zenon_H2df zenon_H2c0 zenon_Hf3 zenon_H2c9 zenon_H389 zenon_H1dd zenon_H6c zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H165 zenon_H78 zenon_H36 zenon_H303 zenon_H109 zenon_H336 zenon_H169 zenon_H1b1 zenon_Ha8 zenon_H3b zenon_Hed zenon_Hc9 zenon_H35 zenon_H16d zenon_Hfe zenon_He4 zenon_He7. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.71/8.86 apply (zenon_L741_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.71/8.86 apply (zenon_L432_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.71/8.86 apply (zenon_L346_); trivial. % 8.71/8.86 apply (zenon_L680_); trivial. % 8.71/8.86 (* end of lemma zenon_L742_ *) % 8.71/8.86 assert (zenon_L743_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.71/8.86 do 0 intro. intros zenon_He7 zenon_He4 zenon_Hfe zenon_H16d zenon_Hed zenon_Ha8 zenon_H169 zenon_H336 zenon_H303 zenon_H36 zenon_H78 zenon_H165 zenon_H389 zenon_H2c9 zenon_Hf3 zenon_H2c0 zenon_H2df zenon_Ha3 zenon_H276 zenon_Had zenon_H67 zenon_H1d9 zenon_H36a zenon_H1dd zenon_H1b1 zenon_H6c zenon_Hcc zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H3b zenon_H7d zenon_H109 zenon_H35. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.71/8.86 apply (zenon_L742_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.71/8.86 apply (zenon_L714_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.71/8.86 apply (zenon_L396_); trivial. % 8.71/8.86 apply (zenon_L106_); trivial. % 8.71/8.86 (* end of lemma zenon_L743_ *) % 8.71/8.86 assert (zenon_L744_ : ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((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)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 8.71/8.86 do 0 intro. intros zenon_Hcb zenon_H27f zenon_Hf1 zenon_H195 zenon_H12b zenon_H10f zenon_H282 zenon_H15a zenon_H35 zenon_H109 zenon_H7d zenon_H3b zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H6c zenon_H1dd zenon_H36a zenon_H1d9 zenon_H67 zenon_Had zenon_H276 zenon_Ha3 zenon_H2df zenon_H2c0 zenon_H2c9 zenon_H389 zenon_H165 zenon_H78 zenon_H36 zenon_H303 zenon_H336 zenon_H169 zenon_Ha8 zenon_Hed zenon_H16d zenon_Hfe zenon_He4 zenon_He7 zenon_H1b1 zenon_Hf3. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H389); [ zenon_intro zenon_H358 | zenon_intro zenon_H38a ]. % 8.71/8.86 apply (zenon_L726_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H38a); [ zenon_intro zenon_H2a | zenon_intro zenon_H38b ]. % 8.71/8.86 apply (zenon_L307_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H38b); [ zenon_intro zenon_Hcc | zenon_intro zenon_Ha2 ]. % 8.71/8.86 apply (zenon_L743_); trivial. % 8.71/8.86 apply (zenon_L559_); trivial. % 8.71/8.86 (* end of lemma zenon_L744_ *) % 8.71/8.86 assert (zenon_L745_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.71/8.86 do 0 intro. intros zenon_H322 zenon_Hf3 zenon_He7 zenon_Hfe zenon_H16d zenon_Hed zenon_H169 zenon_H336 zenon_H303 zenon_H36 zenon_H78 zenon_H165 zenon_H389 zenon_H2c9 zenon_H2c0 zenon_H2df zenon_Ha3 zenon_H276 zenon_Had zenon_H67 zenon_H1d9 zenon_H36a zenon_H1dd zenon_H6c zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H7d zenon_H109 zenon_H15a zenon_H282 zenon_H12b zenon_H27f zenon_Hcb zenon_H1b1 zenon_Ha8 zenon_H3b zenon_H9a zenon_H105 zenon_H10f zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff zenon_H195. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H323 ]. % 8.71/8.86 apply (zenon_L744_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H324 ]. % 8.71/8.86 apply (zenon_L719_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_Hbd | zenon_intro zenon_He8 ]. % 8.71/8.86 apply (zenon_L513_); trivial. % 8.71/8.86 apply (zenon_L687_); trivial. % 8.71/8.86 (* end of lemma zenon_L745_ *) % 8.71/8.86 assert (zenon_L746_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (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)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.71/8.86 do 0 intro. intros zenon_H11f zenon_H31 zenon_H78 zenon_H322 zenon_He7 zenon_H16d zenon_Hed zenon_H169 zenon_H336 zenon_H303 zenon_H36 zenon_H2c0 zenon_H2df zenon_Ha3 zenon_H276 zenon_Had zenon_H67 zenon_H1d9 zenon_H36a zenon_H109 zenon_H12b zenon_H27f zenon_H3b zenon_H9a zenon_H329 zenon_Hf3 zenon_H1b1 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H15a zenon_H6c zenon_H1dd zenon_H2c9 zenon_Hcb zenon_H389 zenon_Hb0 zenon_H145 zenon_H192 zenon_H165 zenon_H282 zenon_H7d zenon_Ha8 zenon_H105 zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff zenon_H195. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.71/8.86 apply (zenon_L4_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.71/8.86 apply (zenon_L263_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hfe | zenon_intro zenon_H32a ]. % 8.71/8.86 apply (zenon_L745_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H108 | zenon_intro zenon_H32b ]. % 8.71/8.86 apply (zenon_L584_); trivial. % 8.71/8.86 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H3c | zenon_intro zenon_He8 ]. % 8.71/8.86 apply (zenon_L65_); trivial. % 8.71/8.86 apply (zenon_L687_); trivial. % 8.71/8.86 apply (zenon_L730_); trivial. % 8.71/8.86 (* end of lemma zenon_L746_ *) % 8.71/8.86 assert (zenon_L747_ : ((op (e0) (e0)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e1)) -> False). % 8.71/8.87 do 0 intro. intros zenon_H66 zenon_H2e8 zenon_Hff zenon_He4 zenon_H35 zenon_Hd0 zenon_H105 zenon_H7d zenon_H282 zenon_H165 zenon_H192 zenon_H145 zenon_Hb0 zenon_H389 zenon_Hcb zenon_H2c9 zenon_H1dd zenon_H6c zenon_H15a zenon_H164 zenon_H1f zenon_H2e2 zenon_H1b1 zenon_Hf3 zenon_H329 zenon_H9a zenon_H27f zenon_H12b zenon_H109 zenon_H36a zenon_H1d9 zenon_H67 zenon_Had zenon_H2df zenon_H2c0 zenon_H36 zenon_H303 zenon_H336 zenon_H169 zenon_Hed zenon_H16d zenon_He7 zenon_H322 zenon_H78 zenon_H31 zenon_H11f zenon_H134 zenon_H90 zenon_H29f zenon_H1e zenon_H25 zenon_H300 zenon_Ha8 zenon_H3b zenon_Ha3 zenon_Hf6. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.71/8.87 apply (zenon_L739_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.71/8.87 apply (zenon_L258_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.71/8.87 apply (zenon_L346_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2e8); [ zenon_intro zenon_H276 | zenon_intro zenon_H2e9 ]. % 8.71/8.87 apply (zenon_L746_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2e9); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H2ea ]. % 8.71/8.87 apply (zenon_L734_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_H99 | zenon_intro zenon_H98 ]. % 8.71/8.87 apply (zenon_L346_); trivial. % 8.71/8.87 apply (zenon_L57_); trivial. % 8.71/8.87 (* end of lemma zenon_L747_ *) % 8.71/8.87 assert (zenon_L748_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.71/8.87 do 0 intro. intros zenon_H137 zenon_H7d zenon_H35 zenon_H3b zenon_H94 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H6c zenon_H1dd zenon_H66 zenon_H2e8 zenon_Hff zenon_He4 zenon_Hd0 zenon_H105 zenon_H282 zenon_H165 zenon_H192 zenon_H145 zenon_H389 zenon_Hcb zenon_H2c9 zenon_Hf3 zenon_H329 zenon_H9a zenon_H27f zenon_H12b zenon_H109 zenon_H36a zenon_H1d9 zenon_H67 zenon_Had zenon_H2df zenon_H2c0 zenon_H36 zenon_H303 zenon_H336 zenon_H169 zenon_Hed zenon_H16d zenon_He7 zenon_H322 zenon_H78 zenon_H31 zenon_H11f zenon_H134 zenon_H90 zenon_H29f zenon_H25 zenon_H300 zenon_Ha8 zenon_H10c zenon_Ha3 zenon_H1b1. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.71/8.87 apply (zenon_L738_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.71/8.87 apply (zenon_L5_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.71/8.87 apply (zenon_L19_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.71/8.87 apply (zenon_L110_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.71/8.87 apply (zenon_L396_); trivial. % 8.71/8.87 apply (zenon_L747_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.71/8.87 apply (zenon_L714_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.71/8.87 apply (zenon_L28_); trivial. % 8.71/8.87 apply (zenon_L584_); trivial. % 8.71/8.87 apply (zenon_L553_); trivial. % 8.71/8.87 (* end of lemma zenon_L748_ *) % 8.71/8.87 assert (zenon_L749_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 8.71/8.87 do 0 intro. intros zenon_H10c zenon_H78 zenon_Hac zenon_Hcb zenon_H6c zenon_H94 zenon_H3b zenon_H35 zenon_H7d. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.71/8.87 apply (zenon_L305_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.71/8.87 apply (zenon_L45_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.71/8.87 apply (zenon_L28_); trivial. % 8.71/8.87 apply (zenon_L584_); trivial. % 8.71/8.87 (* end of lemma zenon_L749_ *) % 8.71/8.87 assert (zenon_L750_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (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) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.71/8.87 do 0 intro. intros zenon_H36a zenon_Hf3 zenon_H1b1 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H15a zenon_H6c zenon_H1dd zenon_H2c9 zenon_H389 zenon_H66 zenon_Hb0 zenon_H3b zenon_H329 zenon_H358 zenon_Hcb zenon_H27f zenon_Hf1 zenon_Hed zenon_H16d zenon_He7 zenon_H12b zenon_H282 zenon_H7d zenon_Ha8 zenon_H105 zenon_H10f zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.71/8.87 apply (zenon_L715_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.71/8.87 apply (zenon_L258_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.71/8.87 apply (zenon_L346_); trivial. % 8.71/8.87 apply (zenon_L727_); trivial. % 8.71/8.87 (* end of lemma zenon_L750_ *) % 8.71/8.87 assert (zenon_L751_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (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 (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (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) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 8.71/8.87 do 0 intro. intros zenon_H10c zenon_Hff zenon_He4 zenon_Hd0 zenon_H105 zenon_Ha8 zenon_H282 zenon_H12b zenon_He7 zenon_H16d zenon_Hed zenon_Hf1 zenon_H27f zenon_H358 zenon_H329 zenon_H66 zenon_H389 zenon_H2c9 zenon_H1dd zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H1b1 zenon_Hf3 zenon_H36a zenon_H78 zenon_H11f zenon_H31 zenon_H67 zenon_H145 zenon_H192 zenon_H137 zenon_H285 zenon_Hcb zenon_H6c zenon_H94 zenon_H3b zenon_H35 zenon_H7d. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H143 | zenon_intro zenon_H286 ]. % 8.71/8.87 apply (zenon_L673_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H165 | zenon_intro zenon_H287 ]. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.71/8.87 apply (zenon_L715_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.71/8.87 apply (zenon_L258_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.71/8.87 apply (zenon_L346_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.71/8.87 apply (zenon_L4_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.71/8.87 apply (zenon_L263_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.71/8.87 apply (zenon_L727_); trivial. % 8.71/8.87 apply (zenon_L730_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H80 | zenon_intro zenon_H10f ]. % 8.71/8.87 apply (zenon_L40_); trivial. % 8.71/8.87 apply (zenon_L750_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.71/8.87 apply (zenon_L45_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.71/8.87 apply (zenon_L28_); trivial. % 8.71/8.87 apply (zenon_L584_); trivial. % 8.71/8.87 (* end of lemma zenon_L751_ *) % 8.71/8.87 assert (zenon_L752_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (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) (e0)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.71/8.87 do 0 intro. intros zenon_H336 zenon_H36 zenon_H7d zenon_H35 zenon_H3b zenon_H94 zenon_H6c zenon_Hcb zenon_H285 zenon_H137 zenon_H192 zenon_H145 zenon_H67 zenon_H31 zenon_H11f zenon_H78 zenon_H36a zenon_Hf3 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H1dd zenon_H2c9 zenon_H389 zenon_H66 zenon_H329 zenon_H358 zenon_H27f zenon_Hf1 zenon_Hed zenon_H16d zenon_He7 zenon_H12b zenon_H282 zenon_Ha8 zenon_H105 zenon_Hd0 zenon_He4 zenon_Hff zenon_H10c zenon_Ha3 zenon_H1b1. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.71/8.87 apply (zenon_L656_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.71/8.87 apply (zenon_L5_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.71/8.87 apply (zenon_L751_); trivial. % 8.71/8.87 apply (zenon_L553_); trivial. % 8.71/8.87 (* end of lemma zenon_L752_ *) % 8.71/8.87 assert (zenon_L753_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (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) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 8.71/8.87 do 0 intro. intros zenon_H36a zenon_Hf3 zenon_H1b1 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H15a zenon_H6c zenon_H1dd zenon_H2c9 zenon_H389 zenon_H66 zenon_Hb0 zenon_Ha8 zenon_H3b zenon_H282 zenon_H10f zenon_H12b zenon_He7 zenon_He4 zenon_Hfe zenon_H16d zenon_H35 zenon_Hed zenon_Hf1 zenon_H27f zenon_Hcb zenon_H358. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.71/8.87 apply (zenon_L715_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.71/8.87 apply (zenon_L258_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.71/8.87 apply (zenon_L346_); trivial. % 8.71/8.87 apply (zenon_L726_); trivial. % 8.71/8.87 (* end of lemma zenon_L753_ *) % 8.71/8.87 assert (zenon_L754_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (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 (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.71/8.87 do 0 intro. intros zenon_H322 zenon_H358 zenon_Hcb zenon_H27f zenon_Hed zenon_H16d zenon_Hfe zenon_He7 zenon_H12b zenon_H282 zenon_Hb0 zenon_H66 zenon_H389 zenon_H2c9 zenon_H1dd zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_Hf3 zenon_H36a zenon_H1b1 zenon_Ha8 zenon_H3b zenon_H9a zenon_H105 zenon_H10f zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff zenon_H195. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H323 ]. % 8.71/8.87 apply (zenon_L753_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H324 ]. % 8.71/8.87 apply (zenon_L719_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_Hbd | zenon_intro zenon_He8 ]. % 8.71/8.87 apply (zenon_L513_); trivial. % 8.71/8.87 apply (zenon_L687_); trivial. % 8.71/8.87 (* end of lemma zenon_L754_ *) % 8.71/8.87 assert (zenon_L755_ : (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (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 (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.71/8.87 do 0 intro. intros zenon_Ha3 zenon_H322 zenon_H358 zenon_Hcb zenon_H27f zenon_Hed zenon_H16d zenon_Hfe zenon_He7 zenon_H12b zenon_H282 zenon_Hb0 zenon_H66 zenon_H389 zenon_H2c9 zenon_H1dd zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_Hf3 zenon_H36a zenon_H1b1 zenon_Ha8 zenon_H3b zenon_H9a zenon_H105 zenon_H10f zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.71/8.87 apply (zenon_L713_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.71/8.87 apply (zenon_L395_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.71/8.87 apply (zenon_L346_); trivial. % 8.71/8.87 apply (zenon_L754_); trivial. % 8.71/8.87 (* end of lemma zenon_L755_ *) % 8.71/8.87 assert (zenon_L756_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (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 (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.71/8.87 do 0 intro. intros zenon_H285 zenon_H137 zenon_H7d zenon_H192 zenon_H145 zenon_H329 zenon_H67 zenon_H31 zenon_H11f zenon_H78 zenon_Ha3 zenon_H322 zenon_H358 zenon_Hcb zenon_H27f zenon_Hed zenon_H16d zenon_Hfe zenon_He7 zenon_H12b zenon_H282 zenon_Hb0 zenon_H66 zenon_H389 zenon_H2c9 zenon_H1dd zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_Hf3 zenon_H36a zenon_H1b1 zenon_Ha8 zenon_H3b zenon_H9a zenon_H105 zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H143 | zenon_intro zenon_H286 ]. % 8.71/8.87 apply (zenon_L673_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H165 | zenon_intro zenon_H287 ]. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.71/8.87 apply (zenon_L713_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.71/8.87 apply (zenon_L395_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.71/8.87 apply (zenon_L346_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.71/8.87 apply (zenon_L4_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.71/8.87 apply (zenon_L263_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.71/8.87 apply (zenon_L754_); trivial. % 8.71/8.87 apply (zenon_L730_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H80 | zenon_intro zenon_H10f ]. % 8.71/8.87 apply (zenon_L40_); trivial. % 8.71/8.87 apply (zenon_L755_); trivial. % 8.71/8.87 (* end of lemma zenon_L756_ *) % 8.71/8.87 assert (zenon_L757_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.71/8.87 do 0 intro. intros zenon_H336 zenon_H1f6 zenon_H303 zenon_H109 zenon_H36 zenon_Ha8 zenon_H7d zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H6c zenon_H1dd zenon_H285 zenon_H137 zenon_H192 zenon_H145 zenon_H329 zenon_H67 zenon_H31 zenon_H11f zenon_H78 zenon_H322 zenon_H358 zenon_H27f zenon_Hed zenon_H16d zenon_Hfe zenon_He7 zenon_H12b zenon_H282 zenon_Hb0 zenon_H66 zenon_H389 zenon_H2c9 zenon_Hf3 zenon_H36a zenon_H3b zenon_H9a zenon_H105 zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff zenon_H2c0 zenon_Ha3 zenon_H1b1. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.71/8.87 apply (zenon_L725_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.71/8.87 apply (zenon_L5_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_Hcb | zenon_intro zenon_H2c4 ]. % 8.71/8.87 apply (zenon_L756_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H2c5 ]. % 8.71/8.87 apply (zenon_L714_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1d8 ]. % 8.71/8.87 apply (zenon_L149_); trivial. % 8.71/8.87 apply (zenon_L719_); trivial. % 8.71/8.87 apply (zenon_L553_); trivial. % 8.71/8.87 (* end of lemma zenon_L757_ *) % 8.71/8.87 assert (zenon_L758_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 8.71/8.87 do 0 intro. intros zenon_H11f zenon_H195 zenon_Hff zenon_He4 zenon_H35 zenon_Hd0 zenon_H105 zenon_H9a zenon_H3b zenon_Ha8 zenon_H27f zenon_H12b zenon_H109 zenon_H7d zenon_H36a zenon_H1d9 zenon_H67 zenon_Had zenon_H276 zenon_Ha3 zenon_H2df zenon_H2c0 zenon_H78 zenon_H36 zenon_H303 zenon_H336 zenon_H169 zenon_Hed zenon_H16d zenon_He7 zenon_H322 zenon_H282 zenon_H165 zenon_H192 zenon_Hfe zenon_H145 zenon_Hb0 zenon_H389 zenon_Hcb zenon_H2c9 zenon_H1dd zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H1b1 zenon_Hf3. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.71/8.87 apply (zenon_L394_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.71/8.87 apply (zenon_L263_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.71/8.87 apply (zenon_L745_); trivial. % 8.71/8.87 apply (zenon_L729_); trivial. % 8.71/8.87 (* end of lemma zenon_L758_ *) % 8.71/8.87 assert (zenon_L759_ : (~((e1) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.71/8.87 do 0 intro. intros zenon_Ha3 zenon_H3b zenon_H300 zenon_H25 zenon_H29f zenon_H90 zenon_H134 zenon_H11f zenon_Hff zenon_He4 zenon_H35 zenon_Hd0 zenon_H105 zenon_H9a zenon_H27f zenon_H12b zenon_H109 zenon_H36a zenon_H1d9 zenon_H67 zenon_Had zenon_H2df zenon_H2c0 zenon_H78 zenon_H36 zenon_H303 zenon_H336 zenon_H169 zenon_Hed zenon_H16d zenon_He7 zenon_H322 zenon_H282 zenon_H165 zenon_H192 zenon_Hfe zenon_H145 zenon_Hb0 zenon_H389 zenon_H2c9 zenon_Hf3 zenon_H2e8 zenon_H66 zenon_H1dd zenon_H6c zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H15a zenon_H7d zenon_Ha8 zenon_H1b1. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_Hcb | zenon_intro zenon_H2c4 ]. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.71/8.87 apply (zenon_L19_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.71/8.87 apply (zenon_L110_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.71/8.87 apply (zenon_L396_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.71/8.87 apply (zenon_L715_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.71/8.87 apply (zenon_L395_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.71/8.87 apply (zenon_L346_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2e8); [ zenon_intro zenon_H276 | zenon_intro zenon_H2e9 ]. % 8.71/8.87 apply (zenon_L758_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2e9); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H2ea ]. % 8.71/8.87 apply (zenon_L734_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_H99 | zenon_intro zenon_H98 ]. % 8.71/8.87 apply (zenon_L346_); trivial. % 8.71/8.87 apply (zenon_L57_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H2c5 ]. % 8.71/8.87 apply (zenon_L714_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1d8 ]. % 8.71/8.87 apply (zenon_L149_); trivial. % 8.71/8.87 apply (zenon_L719_); trivial. % 8.71/8.87 (* end of lemma zenon_L759_ *) % 8.71/8.87 assert (zenon_L760_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (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 (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.71/8.87 do 0 intro. intros zenon_H35d zenon_H1b1 zenon_Hc2 zenon_H137 zenon_Ha8 zenon_H7d zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H6c zenon_H1dd zenon_H66 zenon_H2e8 zenon_Hf3 zenon_H2c9 zenon_H389 zenon_Hb0 zenon_H145 zenon_Hfe zenon_H192 zenon_H282 zenon_H322 zenon_He7 zenon_H16d zenon_Hed zenon_H169 zenon_H336 zenon_H303 zenon_H36 zenon_H78 zenon_H2c0 zenon_H2df zenon_H1d9 zenon_H36a zenon_H109 zenon_H12b zenon_H27f zenon_H9a zenon_H105 zenon_Hd0 zenon_He4 zenon_Hff zenon_H11f zenon_H134 zenon_H90 zenon_H29f zenon_H25 zenon_H300 zenon_H3b zenon_Ha3 zenon_H1f6 zenon_H285 zenon_H329 zenon_H31 zenon_H35e zenon_H67 zenon_H35. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H35d); [ zenon_intro zenon_Hac | zenon_intro zenon_H35f ]. % 8.71/8.87 apply (zenon_L305_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_H358 | zenon_intro zenon_H360 ]. % 8.71/8.87 apply (zenon_L757_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Had | zenon_intro zenon_Hd1 ]. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.71/8.87 apply (zenon_L1_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.71/8.87 apply (zenon_L757_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.71/8.87 apply (zenon_L738_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.71/8.87 apply (zenon_L5_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.71/8.87 apply (zenon_L759_); trivial. % 8.71/8.87 apply (zenon_L553_); trivial. % 8.71/8.87 apply (zenon_L685_); trivial. % 8.71/8.87 apply (zenon_L263_); trivial. % 8.71/8.87 (* end of lemma zenon_L760_ *) % 8.71/8.87 assert (zenon_L761_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (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) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 8.71/8.87 do 0 intro. intros zenon_H285 zenon_H137 zenon_H145 zenon_H192 zenon_H67 zenon_H31 zenon_H11f zenon_H78 zenon_H36a zenon_Hf3 zenon_H1b1 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H15a zenon_H6c zenon_H1dd zenon_H2c9 zenon_H389 zenon_H66 zenon_Hb0 zenon_Ha8 zenon_H3b zenon_H282 zenon_H12b zenon_He7 zenon_He4 zenon_Hfe zenon_H16d zenon_H35 zenon_Hed zenon_Hf1 zenon_H27f zenon_Hcb zenon_H358. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H143 | zenon_intro zenon_H286 ]. % 8.71/8.87 apply (zenon_L673_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H165 | zenon_intro zenon_H287 ]. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.71/8.87 apply (zenon_L715_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.71/8.87 apply (zenon_L258_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.71/8.87 apply (zenon_L346_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.71/8.87 apply (zenon_L4_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.71/8.87 apply (zenon_L263_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.71/8.87 apply (zenon_L726_); trivial. % 8.71/8.87 apply (zenon_L729_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H80 | zenon_intro zenon_H10f ]. % 8.71/8.87 apply (zenon_L40_); trivial. % 8.71/8.87 apply (zenon_L753_); trivial. % 8.71/8.87 (* end of lemma zenon_L761_ *) % 8.71/8.87 assert (zenon_L762_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (op (e0) (e1))) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.71/8.87 do 0 intro. intros zenon_H336 zenon_H2aa zenon_H36 zenon_H7d zenon_H35 zenon_H3b zenon_H94 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H6c zenon_H1dd zenon_H2c0 zenon_H358 zenon_H27f zenon_Hf1 zenon_Hed zenon_H16d zenon_Hfe zenon_He4 zenon_He7 zenon_H12b zenon_H282 zenon_H389 zenon_H2c9 zenon_Hf3 zenon_H36a zenon_H78 zenon_H11f zenon_H31 zenon_H67 zenon_H192 zenon_H145 zenon_H285 zenon_H109 zenon_H137 zenon_H66 zenon_H303 zenon_Ha8 zenon_H10c zenon_Ha3 zenon_H1b1. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.71/8.87 apply (zenon_L527_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.71/8.87 apply (zenon_L5_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_Hcb | zenon_intro zenon_H2c4 ]. % 8.71/8.87 apply (zenon_L761_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H2c5 ]. % 8.71/8.87 apply (zenon_L724_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1d8 ]. % 8.71/8.87 apply (zenon_L149_); trivial. % 8.71/8.87 apply (zenon_L719_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.71/8.87 apply (zenon_L714_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.71/8.87 apply (zenon_L28_); trivial. % 8.71/8.87 apply (zenon_L584_); trivial. % 8.71/8.87 apply (zenon_L553_); trivial. % 8.71/8.87 (* end of lemma zenon_L762_ *) % 8.71/8.87 assert (zenon_L763_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (((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)))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.71/8.87 do 0 intro. intros zenon_H336 zenon_Ha8 zenon_H165 zenon_H303 zenon_H66 zenon_H137 zenon_H7d zenon_H109 zenon_H2c0 zenon_H36 zenon_H35 zenon_Hfe zenon_Hd0 zenon_H3b zenon_H94 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H6c zenon_H1dd zenon_Hac zenon_H78 zenon_H10c zenon_Ha3 zenon_H1b1. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.71/8.87 apply (zenon_L738_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.71/8.87 apply (zenon_L5_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.71/8.87 apply (zenon_L305_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.71/8.87 apply (zenon_L714_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.71/8.87 apply (zenon_L28_); trivial. % 8.71/8.87 apply (zenon_L88_); trivial. % 8.71/8.87 apply (zenon_L553_); trivial. % 8.71/8.87 (* end of lemma zenon_L763_ *) % 8.71/8.87 assert (zenon_L764_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (op (e0) (e0))) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (op (e0) (e1))) = (e1))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.71/8.87 do 0 intro. intros zenon_H35e zenon_H12e zenon_H285 zenon_H145 zenon_H192 zenon_H67 zenon_H31 zenon_H11f zenon_H36a zenon_Hf3 zenon_H2c9 zenon_H389 zenon_H282 zenon_H12b zenon_He7 zenon_He4 zenon_H16d zenon_Hed zenon_Hf1 zenon_H27f zenon_H2aa zenon_Ha3 zenon_H10c zenon_H78 zenon_Hac zenon_H1dd zenon_H6c zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H94 zenon_H3b zenon_Hd0 zenon_Hfe zenon_H35 zenon_H36 zenon_H2c0 zenon_H109 zenon_H7d zenon_H137 zenon_H66 zenon_H303 zenon_Ha8 zenon_H336 zenon_Hc2 zenon_H1b1. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.71/8.87 apply (zenon_L76_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.71/8.87 apply (zenon_L762_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.71/8.87 apply (zenon_L763_); trivial. % 8.71/8.87 apply (zenon_L685_); trivial. % 8.71/8.87 (* end of lemma zenon_L764_ *) % 8.71/8.87 assert (zenon_L765_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (op (e0) (e1))) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.71/8.87 do 0 intro. intros zenon_H336 zenon_H2aa zenon_H36 zenon_H35 zenon_H192 zenon_Hc9 zenon_Ha3 zenon_H1b1. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.71/8.87 apply (zenon_L527_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.71/8.87 apply (zenon_L5_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.71/8.87 apply (zenon_L157_); trivial. % 8.71/8.87 apply (zenon_L553_); trivial. % 8.71/8.87 (* end of lemma zenon_L765_ *) % 8.71/8.87 assert (zenon_L766_ : (((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)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.71/8.87 do 0 intro. intros zenon_H322 zenon_H7d zenon_Hf0 zenon_H1b1 zenon_Ha8 zenon_H3b zenon_H9a zenon_H105 zenon_H10f zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff zenon_H195. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H323 ]. % 8.71/8.87 apply (zenon_L55_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H324 ]. % 8.71/8.87 apply (zenon_L719_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_Hbd | zenon_intro zenon_He8 ]. % 8.71/8.87 apply (zenon_L513_); trivial. % 8.71/8.87 apply (zenon_L687_); trivial. % 8.71/8.87 (* end of lemma zenon_L766_ *) % 8.71/8.87 assert (zenon_L767_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.71/8.87 do 0 intro. intros zenon_H36a zenon_H78 zenon_H2c0 zenon_Ha3 zenon_H11f zenon_H31 zenon_H67 zenon_H9a zenon_H3b zenon_Hf0 zenon_H322 zenon_H329 zenon_Hf3 zenon_H1b1 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H15a zenon_H6c zenon_H1dd zenon_H2c9 zenon_Hcb zenon_H389 zenon_Hb0 zenon_H145 zenon_H192 zenon_H165 zenon_H282 zenon_H7d zenon_Ha8 zenon_H105 zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.71/8.87 apply (zenon_L739_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.71/8.87 apply (zenon_L395_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.71/8.87 apply (zenon_L346_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.71/8.87 apply (zenon_L4_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.71/8.87 apply (zenon_L263_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.71/8.87 apply (zenon_L766_); trivial. % 8.71/8.87 apply (zenon_L730_); trivial. % 8.71/8.87 (* end of lemma zenon_L767_ *) % 8.71/8.87 assert (zenon_L768_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (((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)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.71/8.87 do 0 intro. intros zenon_H36a zenon_H358 zenon_Hcb zenon_Ha3 zenon_H15a zenon_H322 zenon_H7d zenon_Hf0 zenon_H1b1 zenon_Ha8 zenon_H3b zenon_H9a zenon_H105 zenon_H10f zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.71/8.87 apply (zenon_L713_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.71/8.87 apply (zenon_L395_); trivial. % 8.71/8.87 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.71/8.87 apply (zenon_L346_); trivial. % 8.71/8.87 apply (zenon_L766_); trivial. % 8.71/8.87 (* end of lemma zenon_L768_ *) % 8.71/8.87 assert (zenon_L769_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (((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 (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (((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)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.72/8.88 do 0 intro. intros zenon_H285 zenon_H137 zenon_H282 zenon_H192 zenon_H145 zenon_Hb0 zenon_H389 zenon_H2c9 zenon_H1dd zenon_H6c zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_Hf3 zenon_H329 zenon_H67 zenon_H31 zenon_H11f zenon_H2c0 zenon_H78 zenon_H36a zenon_H358 zenon_Hcb zenon_Ha3 zenon_H15a zenon_H322 zenon_H7d zenon_Hf0 zenon_H1b1 zenon_Ha8 zenon_H3b zenon_H9a zenon_H105 zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H143 | zenon_intro zenon_H286 ]. % 8.72/8.88 apply (zenon_L673_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H165 | zenon_intro zenon_H287 ]. % 8.72/8.88 apply (zenon_L767_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H80 | zenon_intro zenon_H10f ]. % 8.72/8.88 apply (zenon_L40_); trivial. % 8.72/8.88 apply (zenon_L768_); trivial. % 8.72/8.88 (* end of lemma zenon_L769_ *) % 8.72/8.88 assert (zenon_L770_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (op (e0) (e1))) = (e1))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.72/8.88 do 0 intro. intros zenon_H35e zenon_H285 zenon_H137 zenon_H2aa zenon_Ha3 zenon_H36a zenon_H78 zenon_H2c0 zenon_H11f zenon_H31 zenon_H67 zenon_H9a zenon_H3b zenon_Hf0 zenon_H322 zenon_H329 zenon_Hf3 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H6c zenon_H1dd zenon_H2c9 zenon_Hcb zenon_H389 zenon_Hb0 zenon_H145 zenon_H192 zenon_H282 zenon_H7d zenon_Ha8 zenon_H105 zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff zenon_H36 zenon_H336 zenon_Hc2 zenon_H1b1. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.72/8.88 apply (zenon_L1_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.72/8.88 apply (zenon_L527_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.72/8.88 apply (zenon_L5_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.72/8.88 apply (zenon_L769_); trivial. % 8.72/8.88 apply (zenon_L553_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.72/8.88 apply (zenon_L656_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.72/8.88 apply (zenon_L5_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.72/8.88 apply (zenon_L767_); trivial. % 8.72/8.88 apply (zenon_L553_); trivial. % 8.72/8.88 apply (zenon_L685_); trivial. % 8.72/8.88 (* end of lemma zenon_L770_ *) % 8.72/8.88 assert (zenon_L771_ : (((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)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 8.72/8.88 do 0 intro. intros zenon_H322 zenon_H7d zenon_Hf0 zenon_H1b1 zenon_Ha8 zenon_H3b zenon_H9a zenon_He4 zenon_Hfe. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H323 ]. % 8.72/8.88 apply (zenon_L55_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H324 ]. % 8.72/8.88 apply (zenon_L719_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_Hbd | zenon_intro zenon_He8 ]. % 8.72/8.88 apply (zenon_L513_); trivial. % 8.72/8.88 apply (zenon_L679_); trivial. % 8.72/8.88 (* end of lemma zenon_L771_ *) % 8.72/8.88 assert (zenon_L772_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.72/8.88 do 0 intro. intros zenon_H389 zenon_Hcb zenon_H27f zenon_Hf1 zenon_Hed zenon_H16d zenon_Hfe zenon_He4 zenon_H195 zenon_He7 zenon_H12b zenon_H10f zenon_H282 zenon_H2c9 zenon_H1dd zenon_H1b1 zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H41 zenon_H35. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H389); [ zenon_intro zenon_H358 | zenon_intro zenon_H38a ]. % 8.72/8.88 apply (zenon_L726_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H38a); [ zenon_intro zenon_H2a | zenon_intro zenon_H38b ]. % 8.72/8.88 apply (zenon_L307_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H38b); [ zenon_intro zenon_Hcc | zenon_intro zenon_Ha2 ]. % 8.72/8.88 apply (zenon_L714_); trivial. % 8.72/8.88 apply (zenon_L247_); trivial. % 8.72/8.88 (* end of lemma zenon_L772_ *) % 8.72/8.88 assert (zenon_L773_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 8.72/8.88 do 0 intro. intros zenon_H11f zenon_H31 zenon_H67 zenon_H35 zenon_H41 zenon_H12b zenon_He7 zenon_H195 zenon_He4 zenon_H16d zenon_Hed zenon_Hf1 zenon_H27f zenon_H282 zenon_H165 zenon_H192 zenon_Hfe zenon_H145 zenon_Hb0 zenon_H389 zenon_Hcb zenon_H2c9 zenon_H1dd zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H1b1 zenon_Hf3. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.72/8.88 apply (zenon_L4_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.72/8.88 apply (zenon_L263_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.72/8.88 apply (zenon_L772_); trivial. % 8.72/8.88 apply (zenon_L729_); trivial. % 8.72/8.88 (* end of lemma zenon_L773_ *) % 8.72/8.88 assert (zenon_L774_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.72/8.88 do 0 intro. intros zenon_H322 zenon_Hf3 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H15a zenon_H6c zenon_H1dd zenon_H2c9 zenon_Hcb zenon_H389 zenon_Hb0 zenon_H145 zenon_Hfe zenon_H192 zenon_H165 zenon_H282 zenon_H27f zenon_Hed zenon_H16d zenon_He7 zenon_H12b zenon_H41 zenon_H67 zenon_H31 zenon_H11f zenon_H1b1 zenon_Ha8 zenon_H3b zenon_H9a zenon_H105 zenon_H10f zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff zenon_H195. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H323 ]. % 8.72/8.88 apply (zenon_L773_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H324 ]. % 8.72/8.88 apply (zenon_L719_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_Hbd | zenon_intro zenon_He8 ]. % 8.72/8.88 apply (zenon_L513_); trivial. % 8.72/8.88 apply (zenon_L687_); trivial. % 8.72/8.88 (* end of lemma zenon_L774_ *) % 8.72/8.88 assert (zenon_L775_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 8.72/8.88 do 0 intro. intros zenon_H10c zenon_Hff zenon_He4 zenon_Hd0 zenon_H105 zenon_Ha8 zenon_H282 zenon_H165 zenon_H192 zenon_H145 zenon_H389 zenon_Hcb zenon_H2c9 zenon_Hf3 zenon_H329 zenon_H9a zenon_H3b zenon_H11f zenon_H31 zenon_H67 zenon_H41 zenon_H12b zenon_He7 zenon_H16d zenon_Hed zenon_H27f zenon_H322 zenon_H78 zenon_H175 zenon_H66 zenon_H36a zenon_H1dd zenon_H1b1 zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H154 zenon_H35 zenon_H7d. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.72/8.88 apply (zenon_L715_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.72/8.88 apply (zenon_L258_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.72/8.88 apply (zenon_L346_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.72/8.88 apply (zenon_L193_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.72/8.88 apply (zenon_L263_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hfe | zenon_intro zenon_H32a ]. % 8.72/8.88 apply (zenon_L774_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H108 | zenon_intro zenon_H32b ]. % 8.72/8.88 apply (zenon_L584_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H3c | zenon_intro zenon_He8 ]. % 8.72/8.88 apply (zenon_L65_); trivial. % 8.72/8.88 apply (zenon_L687_); trivial. % 8.72/8.88 apply (zenon_L730_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.72/8.88 apply (zenon_L714_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.72/8.88 apply (zenon_L97_); trivial. % 8.72/8.88 apply (zenon_L584_); trivial. % 8.72/8.88 (* end of lemma zenon_L775_ *) % 8.72/8.88 assert (zenon_L776_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.72/8.88 do 0 intro. intros zenon_H322 zenon_H41 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H15a zenon_H6c zenon_H1dd zenon_H2c9 zenon_H282 zenon_H12b zenon_He7 zenon_Hfe zenon_H16d zenon_Hed zenon_H27f zenon_Hcb zenon_H389 zenon_H1b1 zenon_Ha8 zenon_H3b zenon_H9a zenon_H105 zenon_H10f zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff zenon_H195. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H323 ]. % 8.72/8.88 apply (zenon_L772_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H324 ]. % 8.72/8.88 apply (zenon_L719_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_Hbd | zenon_intro zenon_He8 ]. % 8.72/8.88 apply (zenon_L513_); trivial. % 8.72/8.88 apply (zenon_L687_); trivial. % 8.72/8.88 (* end of lemma zenon_L776_ *) % 8.72/8.88 assert (zenon_L777_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.72/8.88 do 0 intro. intros zenon_H336 zenon_H7d zenon_Hcb zenon_H41 zenon_H192 zenon_Hc9 zenon_Ha3 zenon_H1b1. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.72/8.88 apply (zenon_L656_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.72/8.88 apply (zenon_L9_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.72/8.88 apply (zenon_L157_); trivial. % 8.72/8.88 apply (zenon_L553_); trivial. % 8.72/8.88 (* end of lemma zenon_L777_ *) % 8.72/8.88 assert (zenon_L778_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (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 (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 8.72/8.88 do 0 intro. intros zenon_H11e zenon_H78 zenon_H1e zenon_H192 zenon_H41 zenon_H336 zenon_H90 zenon_H36a zenon_H109 zenon_H7d zenon_H6b zenon_H164 zenon_Ha3 zenon_H303 zenon_H169 zenon_H1b1 zenon_Ha8 zenon_H3b zenon_Hed zenon_Hc9 zenon_H35 zenon_H16d zenon_He4 zenon_He7. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.72/8.88 apply (zenon_L21_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.72/8.88 apply (zenon_L777_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.72/8.88 apply (zenon_L565_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.72/8.88 apply (zenon_L740_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.72/8.88 apply (zenon_L432_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.72/8.88 apply (zenon_L346_); trivial. % 8.72/8.88 apply (zenon_L680_); trivial. % 8.72/8.88 (* end of lemma zenon_L778_ *) % 8.72/8.88 assert (zenon_L779_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 8.72/8.88 do 0 intro. intros zenon_H11e zenon_H78 zenon_H1e zenon_H6b zenon_H90 zenon_H322 zenon_H7d zenon_Hf0 zenon_H1b1 zenon_Ha8 zenon_H3b zenon_H9a zenon_He4. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.72/8.88 apply (zenon_L21_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.72/8.88 apply (zenon_L656_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.72/8.88 apply (zenon_L565_); trivial. % 8.72/8.88 apply (zenon_L771_); trivial. % 8.72/8.88 (* end of lemma zenon_L779_ *) % 8.72/8.88 assert (zenon_L780_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (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) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 8.72/8.88 do 0 intro. intros zenon_H1d9 zenon_H1d7 zenon_H1f6 zenon_H2b8 zenon_H67 zenon_H197 zenon_H74 zenon_H2a2 zenon_H31 zenon_H2d8 zenon_Hff zenon_H19a zenon_H329 zenon_Hc2 zenon_H1d3 zenon_H2b5 zenon_Hd0 zenon_H331 zenon_H173 zenon_H127 zenon_H22d zenon_H2b zenon_Hab zenon_H25 zenon_H22e zenon_H153 zenon_H170 zenon_Hc5 zenon_H29f zenon_H2d2 zenon_H2d4 zenon_H145 zenon_H10c zenon_H32e zenon_H2a5 zenon_H129 zenon_H12b zenon_H6c zenon_H35e zenon_H35d zenon_Hba zenon_Hf3 zenon_H134 zenon_H300 zenon_H2df zenon_H137 zenon_H2a1 zenon_H1dd zenon_H2a4 zenon_H2e8 zenon_Hb4 zenon_H3a zenon_H2fc zenon_H2f3 zenon_H1f zenon_H270 zenon_H2c0 zenon_H1dc zenon_H295 zenon_H2c9 zenon_Hb7 zenon_H150 zenon_H282 zenon_H27f zenon_H285 zenon_Hf9 zenon_H11f zenon_H124 zenon_H36 zenon_H2a3 zenon_Hf8 zenon_H2e2 zenon_H2bf zenon_H105 zenon_H34d zenon_H2f8 zenon_Hbf zenon_H94 zenon_Heb zenon_He7 zenon_H16d zenon_H35 zenon_Hed zenon_H169 zenon_H303 zenon_Ha3 zenon_H164 zenon_H109 zenon_H36a zenon_H336 zenon_H41 zenon_H192 zenon_H11e zenon_H78 zenon_H1e zenon_H6b zenon_H90 zenon_H322 zenon_H7d zenon_H1b1 zenon_Ha8 zenon_H3b zenon_H9a zenon_He4. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.72/8.88 apply (zenon_L725_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.72/8.88 apply (zenon_L639_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.72/8.88 apply (zenon_L778_); trivial. % 8.72/8.88 apply (zenon_L779_); trivial. % 8.72/8.88 (* end of lemma zenon_L780_ *) % 8.72/8.88 assert (zenon_L781_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 8.72/8.88 do 0 intro. intros zenon_H36a zenon_H66 zenon_H78 zenon_Hff zenon_He4 zenon_H35 zenon_Hd0 zenon_H105 zenon_H9a zenon_H3b zenon_Ha8 zenon_H11f zenon_H31 zenon_H67 zenon_H41 zenon_H12b zenon_He7 zenon_H16d zenon_Hed zenon_H27f zenon_H322 zenon_H282 zenon_H165 zenon_H192 zenon_Hfe zenon_H145 zenon_Hb0 zenon_H389 zenon_Hcb zenon_H2c9 zenon_H1dd zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H1b1 zenon_Hf3. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.72/8.88 apply (zenon_L715_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.72/8.88 apply (zenon_L258_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.72/8.88 apply (zenon_L346_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.72/8.88 apply (zenon_L394_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.72/8.88 apply (zenon_L263_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.72/8.88 apply (zenon_L774_); trivial. % 8.72/8.88 apply (zenon_L729_); trivial. % 8.72/8.88 (* end of lemma zenon_L781_ *) % 8.72/8.88 assert (zenon_L782_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.72/8.88 do 0 intro. intros zenon_H36a zenon_H358 zenon_Ha3 zenon_H322 zenon_H41 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H15a zenon_H6c zenon_H1dd zenon_H2c9 zenon_H282 zenon_H12b zenon_He7 zenon_Hfe zenon_H16d zenon_Hed zenon_H27f zenon_Hcb zenon_H389 zenon_H1b1 zenon_Ha8 zenon_H3b zenon_H9a zenon_H105 zenon_H10f zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.72/8.88 apply (zenon_L713_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.72/8.88 apply (zenon_L395_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.72/8.88 apply (zenon_L346_); trivial. % 8.72/8.88 apply (zenon_L776_); trivial. % 8.72/8.88 (* end of lemma zenon_L782_ *) % 8.72/8.88 assert (zenon_L783_ : (((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 (e3) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.72/8.88 do 0 intro. intros zenon_H285 zenon_H137 zenon_Hf3 zenon_Hb0 zenon_H145 zenon_H192 zenon_H67 zenon_H31 zenon_H11f zenon_H66 zenon_H78 zenon_H36a zenon_H358 zenon_Ha3 zenon_H322 zenon_H41 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H15a zenon_H6c zenon_H1dd zenon_H2c9 zenon_H282 zenon_H12b zenon_He7 zenon_Hfe zenon_H16d zenon_Hed zenon_H27f zenon_Hcb zenon_H389 zenon_H1b1 zenon_Ha8 zenon_H3b zenon_H9a zenon_H105 zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H143 | zenon_intro zenon_H286 ]. % 8.72/8.88 apply (zenon_L673_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H165 | zenon_intro zenon_H287 ]. % 8.72/8.88 apply (zenon_L781_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H80 | zenon_intro zenon_H10f ]. % 8.72/8.88 apply (zenon_L40_); trivial. % 8.72/8.88 apply (zenon_L782_); trivial. % 8.72/8.88 (* end of lemma zenon_L783_ *) % 8.72/8.88 assert (zenon_L784_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.72/8.88 do 0 intro. intros zenon_H2c0 zenon_Hff zenon_He4 zenon_H35 zenon_Hd0 zenon_H105 zenon_H9a zenon_H3b zenon_H389 zenon_H27f zenon_Hed zenon_H16d zenon_Hfe zenon_He7 zenon_H12b zenon_H282 zenon_H2c9 zenon_H41 zenon_H322 zenon_Ha3 zenon_H358 zenon_H36a zenon_H78 zenon_H66 zenon_H11f zenon_H31 zenon_H67 zenon_H192 zenon_H145 zenon_Hb0 zenon_Hf3 zenon_H137 zenon_H285 zenon_H1dd zenon_H6c zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H15a zenon_H7d zenon_Ha8 zenon_H1b1. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_Hcb | zenon_intro zenon_H2c4 ]. % 8.72/8.88 apply (zenon_L783_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H2c5 ]. % 8.72/8.88 apply (zenon_L714_); trivial. % 8.72/8.88 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1d8 ]. % 8.72/8.88 apply (zenon_L149_); trivial. % 8.72/8.88 apply (zenon_L719_); trivial. % 8.72/8.88 (* end of lemma zenon_L784_ *) % 8.72/8.88 assert (zenon_L785_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = 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(e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) 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(e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3)))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((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 (e3) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.72/8.89 do 0 intro. intros zenon_H90 zenon_H11e zenon_H336 zenon_H109 zenon_H303 zenon_H169 zenon_Heb zenon_H94 zenon_Hbf zenon_H2f8 zenon_H34d zenon_H2bf zenon_Hf8 zenon_H2a3 zenon_H36 zenon_H124 zenon_Hf9 zenon_H150 zenon_Hb7 zenon_H295 zenon_H1dc zenon_H270 zenon_H2f3 zenon_H2fc zenon_H3a zenon_Hb4 zenon_H2e8 zenon_H2a4 zenon_H2a1 zenon_H2df zenon_H300 zenon_H134 zenon_Hba zenon_H35d zenon_H35e zenon_H129 zenon_H2a5 zenon_H32e zenon_H10c zenon_H2d4 zenon_H2d2 zenon_H29f zenon_Hc5 zenon_H170 zenon_H153 zenon_H22e zenon_H25 zenon_Hab zenon_H2b zenon_H22d zenon_H127 zenon_H173 zenon_H331 zenon_H2b5 zenon_H1d3 zenon_Hc2 zenon_H329 zenon_H19a zenon_H2d8 zenon_H2a2 zenon_H74 zenon_H197 zenon_H2b8 zenon_H1f6 zenon_H1d7 zenon_H1d9 zenon_H47 zenon_Ha8 zenon_H7d zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H6c zenon_H1dd zenon_H285 zenon_H137 zenon_Hf3 zenon_Hb0 zenon_H145 zenon_H192 zenon_H67 zenon_H31 zenon_H11f zenon_H66 zenon_H78 zenon_H36a zenon_H358 zenon_H322 zenon_H41 zenon_H2c9 zenon_H282 zenon_H12b zenon_He7 zenon_Hfe zenon_H16d zenon_Hed zenon_H27f zenon_H389 zenon_H3b zenon_H9a zenon_H105 zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff zenon_H2c0 zenon_Ha3 zenon_H1b1. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.72/8.89 apply (zenon_L780_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.72/8.89 apply (zenon_L10_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.72/8.89 apply (zenon_L784_); trivial. % 8.72/8.89 apply (zenon_L553_); trivial. % 8.72/8.89 (* end of lemma zenon_L785_ *) % 8.72/8.89 assert (zenon_L786_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.72/8.89 do 0 intro. intros zenon_H2c0 zenon_Hf3 zenon_H2c9 zenon_H389 zenon_Hb0 zenon_H145 zenon_Hfe zenon_H192 zenon_H165 zenon_H282 zenon_H322 zenon_H27f zenon_Hed zenon_H16d zenon_He7 zenon_H12b zenon_H41 zenon_H67 zenon_H31 zenon_H11f zenon_H3b zenon_H9a zenon_H105 zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff zenon_H78 zenon_H66 zenon_H36a zenon_H1dd zenon_H6c zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H15a zenon_H7d zenon_Ha8 zenon_H1b1. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_Hcb | zenon_intro zenon_H2c4 ]. % 8.72/8.89 apply (zenon_L781_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H2c5 ]. % 8.72/8.89 apply (zenon_L714_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1d8 ]. % 8.72/8.89 apply (zenon_L149_); trivial. % 8.72/8.89 apply (zenon_L719_); trivial. % 8.72/8.89 (* end of lemma zenon_L786_ *) % 8.72/8.89 assert (zenon_L787_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 8.72/8.89 do 0 intro. intros zenon_H36a zenon_H66 zenon_Ha8 zenon_H3b zenon_H11f zenon_H31 zenon_H67 zenon_H35 zenon_H41 zenon_H12b zenon_He7 zenon_He4 zenon_H16d zenon_Hed zenon_Hf1 zenon_H27f zenon_H282 zenon_H165 zenon_H192 zenon_Hfe zenon_H145 zenon_Hb0 zenon_H389 zenon_Hcb zenon_H2c9 zenon_H1dd zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H1b1 zenon_Hf3. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.72/8.89 apply (zenon_L715_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.72/8.89 apply (zenon_L258_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.72/8.89 apply (zenon_L346_); trivial. % 8.72/8.89 apply (zenon_L773_); trivial. % 8.72/8.89 (* end of lemma zenon_L787_ *) % 8.72/8.89 assert (zenon_L788_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.72/8.89 do 0 intro. intros zenon_H36a zenon_H358 zenon_H169 zenon_Ha8 zenon_H3b zenon_H389 zenon_Hcb zenon_H27f zenon_Hf1 zenon_Hed zenon_H16d zenon_Hfe zenon_He4 zenon_He7 zenon_H12b zenon_H10f zenon_H282 zenon_H2c9 zenon_H1dd zenon_H1b1 zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H41 zenon_H35. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.72/8.89 apply (zenon_L713_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.72/8.89 apply (zenon_L432_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.72/8.89 apply (zenon_L346_); trivial. % 8.72/8.89 apply (zenon_L772_); trivial. % 8.72/8.89 (* end of lemma zenon_L788_ *) % 8.72/8.89 assert (zenon_L789_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((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)))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (op (e1) (e2))) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 8.72/8.89 do 0 intro. intros zenon_H10c zenon_Ha8 zenon_H1f6 zenon_H3b zenon_H303 zenon_H66 zenon_H137 zenon_H7d zenon_H109 zenon_H35 zenon_H285 zenon_Hf3 zenon_H145 zenon_H192 zenon_H67 zenon_H31 zenon_H11f zenon_H78 zenon_H36a zenon_H358 zenon_H169 zenon_H389 zenon_H27f zenon_Hf1 zenon_Hed zenon_H16d zenon_He4 zenon_He7 zenon_H12b zenon_H282 zenon_H2c9 zenon_H41 zenon_H2c0 zenon_H1dd zenon_H1b1 zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H154 zenon_Hd0 zenon_Hfe. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_Hcb | zenon_intro zenon_H2c4 ]. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H143 | zenon_intro zenon_H286 ]. % 8.72/8.89 apply (zenon_L673_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H165 | zenon_intro zenon_H287 ]. % 8.72/8.89 apply (zenon_L787_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H80 | zenon_intro zenon_H10f ]. % 8.72/8.89 apply (zenon_L40_); trivial. % 8.72/8.89 apply (zenon_L788_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H2c5 ]. % 8.72/8.89 apply (zenon_L724_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1d8 ]. % 8.72/8.89 apply (zenon_L198_); trivial. % 8.72/8.89 apply (zenon_L719_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.72/8.89 apply (zenon_L714_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.72/8.89 apply (zenon_L97_); trivial. % 8.72/8.89 apply (zenon_L88_); trivial. % 8.72/8.89 (* end of lemma zenon_L789_ *) % 8.72/8.89 assert (zenon_L790_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.72/8.89 do 0 intro. intros zenon_H2c0 zenon_Hf3 zenon_H2c9 zenon_H389 zenon_Hb0 zenon_H145 zenon_Hfe zenon_H192 zenon_H282 zenon_H27f zenon_Hf1 zenon_Hed zenon_H16d zenon_He4 zenon_He7 zenon_H12b zenon_H41 zenon_H35 zenon_H67 zenon_H31 zenon_H11f zenon_H3b zenon_H66 zenon_H36a zenon_H1dd zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H165 zenon_H78 zenon_Ha8 zenon_H1b1. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_Hcb | zenon_intro zenon_H2c4 ]. % 8.72/8.89 apply (zenon_L787_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H2c5 ]. % 8.72/8.89 apply (zenon_L714_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1d8 ]. % 8.72/8.89 apply (zenon_L626_); trivial. % 8.72/8.89 apply (zenon_L719_); trivial. % 8.72/8.89 (* end of lemma zenon_L790_ *) % 8.72/8.89 assert (zenon_L791_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 8.72/8.89 do 0 intro. intros zenon_H10c zenon_Ha8 zenon_H78 zenon_H165 zenon_H36a zenon_H66 zenon_H11f zenon_H31 zenon_H67 zenon_H41 zenon_H12b zenon_He7 zenon_He4 zenon_H16d zenon_Hed zenon_Hf1 zenon_H27f zenon_H282 zenon_H192 zenon_Hfe zenon_H145 zenon_H389 zenon_H2c9 zenon_Hf3 zenon_H2c0 zenon_H1dd zenon_H1b1 zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H94 zenon_H3b zenon_H35 zenon_H7d. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.72/8.89 apply (zenon_L790_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.72/8.89 apply (zenon_L714_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.72/8.89 apply (zenon_L28_); trivial. % 8.72/8.89 apply (zenon_L584_); trivial. % 8.72/8.89 (* end of lemma zenon_L791_ *) % 8.72/8.89 assert (zenon_L792_ : (((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3)))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.72/8.89 do 0 intro. intros zenon_H336 zenon_H90 zenon_H11e zenon_H47 zenon_Hff zenon_He4 zenon_H35 zenon_Hd0 zenon_H105 zenon_H9a zenon_H3b zenon_Ha8 zenon_Hf0 zenon_H7d zenon_H322 zenon_Hcb zenon_H358 zenon_H36a zenon_H78 zenon_H2c0 zenon_H11f zenon_H31 zenon_H67 zenon_H329 zenon_Hf3 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H6c zenon_H1dd zenon_H2c9 zenon_H389 zenon_Hb0 zenon_H145 zenon_H192 zenon_H282 zenon_H137 zenon_H285 zenon_Ha3 zenon_H1b1. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.72/8.89 apply (zenon_L779_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.72/8.89 apply (zenon_L10_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.72/8.89 apply (zenon_L769_); trivial. % 8.72/8.89 apply (zenon_L553_); trivial. % 8.72/8.89 (* end of lemma zenon_L792_ *) % 8.72/8.89 assert (zenon_L793_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> False). % 8.72/8.89 do 0 intro. intros zenon_H178 zenon_H1f. % 8.72/8.89 apply (zenon_L114_); trivial. % 8.72/8.89 (* end of lemma zenon_L793_ *) % 8.72/8.89 assert (zenon_L794_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> False). % 8.72/8.89 do 0 intro. intros zenon_H1a3 zenon_H137 zenon_H1e. % 8.72/8.89 apply (zenon_and_s _ _ zenon_H1a3). zenon_intro zenon_H24. zenon_intro zenon_H1a4. % 8.72/8.89 apply (zenon_and_s _ _ zenon_H1a4). zenon_intro zenon_H143. zenon_intro zenon_H1a5. % 8.72/8.89 apply (zenon_L673_); trivial. % 8.72/8.89 (* end of lemma zenon_L794_ *) % 8.72/8.89 assert (zenon_L795_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> False). % 8.72/8.89 do 0 intro. intros zenon_H1a6 zenon_H3a zenon_H3b. % 8.72/8.89 apply (zenon_and_s _ _ zenon_H1a6). zenon_intro zenon_H24. zenon_intro zenon_H1a7. % 8.72/8.89 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H143. zenon_intro zenon_H1a8. % 8.72/8.89 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hbd. zenon_intro zenon_H3c. % 8.72/8.89 apply (zenon_L6_); trivial. % 8.72/8.89 (* end of lemma zenon_L795_ *) % 8.72/8.89 assert (zenon_L796_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((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))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (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)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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 (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.72/8.89 do 0 intro. intros zenon_H1b7 zenon_H36a zenon_Heb zenon_H94 zenon_H11e zenon_Hbf zenon_H322 zenon_H2f8 zenon_H34d zenon_H105 zenon_He4 zenon_H2bf zenon_H2e2 zenon_Hf8 zenon_H2a3 zenon_H36 zenon_H124 zenon_H11f zenon_Hf9 zenon_H285 zenon_H27f zenon_H282 zenon_H150 zenon_Hb7 zenon_H2c9 zenon_H295 zenon_H1dc zenon_H2c0 zenon_H270 zenon_H1f zenon_H16d zenon_H2f3 zenon_H164 zenon_H2fc zenon_H3a zenon_Hb4 zenon_H2e8 zenon_H2a4 zenon_H1dd zenon_H336 zenon_H2a1 zenon_H137 zenon_H2df zenon_H9a zenon_H300 zenon_H90 zenon_H134 zenon_Hf3 zenon_Hba zenon_H35d zenon_H35e zenon_H6c zenon_H12b zenon_H129 zenon_H2a5 zenon_H32e zenon_H10c zenon_H145 zenon_H2d4 zenon_H2d2 zenon_H29f zenon_Hc5 zenon_H170 zenon_H153 zenon_H22e zenon_H25 zenon_Hab zenon_H2b zenon_H22d zenon_H127 zenon_H173 zenon_H331 zenon_Hd0 zenon_H2b5 zenon_H1d3 zenon_Hc2 zenon_H303 zenon_H329 zenon_H78 zenon_H7d zenon_H19a zenon_H192 zenon_H109 zenon_He7 zenon_Hff zenon_H2d8 zenon_H169 zenon_H31 zenon_H2a2 zenon_H74 zenon_H197 zenon_H67 zenon_H2b8 zenon_Ha3 zenon_H1f6 zenon_Ha8 zenon_H1d7 zenon_H1d9. % 8.72/8.89 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_H73. zenon_intro zenon_H1b8. % 8.72/8.89 apply (zenon_L639_); trivial. % 8.72/8.89 (* end of lemma zenon_L796_ *) % 8.72/8.89 assert (zenon_L797_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> False). % 8.72/8.89 do 0 intro. intros zenon_H1bd zenon_H1e zenon_H31. % 8.72/8.89 apply (zenon_and_s _ _ zenon_H1bd). zenon_intro zenon_H73. zenon_intro zenon_H1be. % 8.72/8.89 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_H6b. zenon_intro zenon_H180. % 8.72/8.89 apply (zenon_and_s _ _ zenon_H180). zenon_intro zenon_H14e. zenon_intro zenon_H30. % 8.72/8.89 apply (zenon_L4_); trivial. % 8.72/8.89 (* end of lemma zenon_L797_ *) % 8.72/8.89 assert (zenon_L798_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.72/8.89 do 0 intro. intros zenon_H1cc zenon_H129 zenon_H35. % 8.72/8.89 apply (zenon_and_s _ _ zenon_H1cc). zenon_intro zenon_H29. zenon_intro zenon_H1cd. % 8.72/8.89 apply (zenon_L74_); trivial. % 8.72/8.89 (* end of lemma zenon_L798_ *) % 8.72/8.89 assert (zenon_L799_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> False). % 8.72/8.89 do 0 intro. intros zenon_H1ce zenon_H3a zenon_H3b. % 8.72/8.89 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H29. zenon_intro zenon_H1cf. % 8.72/8.89 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_H15a. zenon_intro zenon_H1a8. % 8.72/8.89 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hbd. zenon_intro zenon_H3c. % 8.72/8.89 apply (zenon_L6_); trivial. % 8.72/8.89 (* end of lemma zenon_L799_ *) % 8.72/8.89 assert (zenon_L800_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 8.72/8.89 do 0 intro. intros zenon_H1ea zenon_H3b zenon_H90. % 8.72/8.89 apply (zenon_and_s _ _ zenon_H1ea). zenon_intro zenon_Hc8. zenon_intro zenon_H1eb. % 8.72/8.89 apply (zenon_and_s _ _ zenon_H1eb). zenon_intro zenon_H7e. zenon_intro zenon_H177. % 8.72/8.89 apply (zenon_L565_); trivial. % 8.72/8.89 (* end of lemma zenon_L800_ *) % 8.72/8.89 assert (zenon_L801_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> False). % 8.72/8.89 do 0 intro. intros zenon_H1ec zenon_H1e zenon_H1f. % 8.72/8.89 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_Hc8. zenon_intro zenon_H1ed. % 8.72/8.89 apply (zenon_and_s _ _ zenon_H1ed). zenon_intro zenon_H7e. zenon_intro zenon_H17a. % 8.72/8.89 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_Hac. zenon_intro zenon_H1d. % 8.72/8.89 apply (zenon_L1_); trivial. % 8.72/8.89 (* end of lemma zenon_L801_ *) % 8.72/8.89 assert (zenon_L802_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((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 (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.72/8.89 do 0 intro. intros zenon_H2c0 zenon_H6b zenon_H35 zenon_H109 zenon_H7d zenon_H3b zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H6c zenon_H1dd zenon_H137 zenon_H66 zenon_H303 zenon_H1f6 zenon_H201 zenon_Ha8 zenon_H1b1. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_Hcb | zenon_intro zenon_H2c4 ]. % 8.72/8.89 apply (zenon_L656_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H2c5 ]. % 8.72/8.89 apply (zenon_L724_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1d8 ]. % 8.72/8.89 apply (zenon_L217_); trivial. % 8.72/8.89 apply (zenon_L719_); trivial. % 8.72/8.89 (* end of lemma zenon_L802_ *) % 8.72/8.89 assert (zenon_L803_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (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) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = 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= (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 8.72/8.89 do 0 intro. intros zenon_H201 zenon_H1d9 zenon_H1d7 zenon_H1f6 zenon_H2b8 zenon_H67 zenon_H197 zenon_H74 zenon_H2a2 zenon_H31 zenon_H2d8 zenon_Hff zenon_H19a zenon_H329 zenon_Hc2 zenon_H1d3 zenon_H2b5 zenon_Hd0 zenon_H331 zenon_H173 zenon_H127 zenon_H22d zenon_H2b zenon_Hab zenon_H25 zenon_H22e zenon_H153 zenon_H170 zenon_Hc5 zenon_H29f zenon_H2d2 zenon_H2d4 zenon_H145 zenon_H10c zenon_H32e zenon_H2a5 zenon_H129 zenon_H12b zenon_H6c zenon_H35e zenon_H35d zenon_Hba zenon_Hf3 zenon_H134 zenon_H300 zenon_H2df zenon_H137 zenon_H2a1 zenon_H1dd zenon_H2a4 zenon_H2e8 zenon_Hb4 zenon_H3a zenon_H2fc zenon_H2f3 zenon_H1f zenon_H270 zenon_H2c0 zenon_H1dc zenon_H295 zenon_H2c9 zenon_Hb7 zenon_H150 zenon_H282 zenon_H27f zenon_H285 zenon_Hf9 zenon_H11f zenon_H124 zenon_H36 zenon_H2a3 zenon_Hf8 zenon_H2e2 zenon_H2bf zenon_H105 zenon_H34d zenon_H2f8 zenon_Hbf zenon_H94 zenon_Heb zenon_He7 zenon_H16d zenon_H35 zenon_Hed zenon_H169 zenon_H303 zenon_Ha3 zenon_H164 zenon_H109 zenon_H36a zenon_H336 zenon_H41 zenon_H192 zenon_H11e zenon_H78 zenon_H1e zenon_H6b zenon_H90 zenon_H322 zenon_H7d zenon_H1b1 zenon_Ha8 zenon_H3b zenon_H9a zenon_He4. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.72/8.89 apply (zenon_L802_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.72/8.89 apply (zenon_L639_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.72/8.89 apply (zenon_L778_); trivial. % 8.72/8.89 apply (zenon_L779_); trivial. % 8.72/8.89 (* end of lemma zenon_L803_ *) % 8.72/8.89 assert (zenon_L804_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.72/8.89 do 0 intro. intros zenon_H329 zenon_H9a zenon_H3b zenon_Ha8 zenon_H1b1 zenon_H389 zenon_Hcb zenon_H27f zenon_Hed zenon_H16d zenon_He7 zenon_H12b zenon_H282 zenon_H2c9 zenon_H1dd zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H41 zenon_H322 zenon_H7d zenon_H3a zenon_H201 zenon_H105 zenon_H10f zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff zenon_H195. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hfe | zenon_intro zenon_H32a ]. % 8.72/8.89 apply (zenon_L776_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H108 | zenon_intro zenon_H32b ]. % 8.72/8.89 apply (zenon_L584_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H3c | zenon_intro zenon_He8 ]. % 8.72/8.89 apply (zenon_L531_); trivial. % 8.72/8.89 apply (zenon_L687_); trivial. % 8.72/8.89 (* end of lemma zenon_L804_ *) % 8.72/8.89 assert (zenon_L805_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 8.72/8.89 do 0 intro. intros zenon_H10c zenon_Hff zenon_He4 zenon_Hd0 zenon_H105 zenon_Ha8 zenon_H282 zenon_H165 zenon_H192 zenon_H145 zenon_H389 zenon_Hcb zenon_H2c9 zenon_Hf3 zenon_H329 zenon_H9a zenon_H27f zenon_Hed zenon_H16d zenon_He7 zenon_H12b zenon_H41 zenon_H322 zenon_H3a zenon_H201 zenon_H67 zenon_H31 zenon_H11f zenon_Ha3 zenon_H36a zenon_H1dd zenon_H1b1 zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H94 zenon_H3b zenon_H35 zenon_H7d. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.72/8.89 apply (zenon_L715_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.72/8.89 apply (zenon_L395_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.72/8.89 apply (zenon_L346_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.72/8.89 apply (zenon_L4_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.72/8.89 apply (zenon_L263_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.72/8.89 apply (zenon_L804_); trivial. % 8.72/8.89 apply (zenon_L730_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.72/8.89 apply (zenon_L714_); trivial. % 8.72/8.89 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.72/8.89 apply (zenon_L28_); trivial. % 8.72/8.89 apply (zenon_L584_); trivial. % 8.72/8.89 (* end of lemma zenon_L805_ *) % 8.72/8.89 assert (zenon_L806_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((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 (e3) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (op (e1) (e1))) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.72/8.90 do 0 intro. intros zenon_H336 zenon_H201 zenon_H1f6 zenon_H303 zenon_H109 zenon_Ha8 zenon_H7d zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H6c zenon_H1dd zenon_H285 zenon_H137 zenon_Hf3 zenon_Hb0 zenon_H145 zenon_H192 zenon_H67 zenon_H31 zenon_H11f zenon_H66 zenon_H78 zenon_H36a zenon_H358 zenon_H322 zenon_H41 zenon_H2c9 zenon_H282 zenon_H12b zenon_He7 zenon_Hfe zenon_H16d zenon_Hed zenon_H27f zenon_H389 zenon_H3b zenon_H9a zenon_H105 zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff zenon_H2c0 zenon_Ha3 zenon_H1b1. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.72/8.90 apply (zenon_L802_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.72/8.90 apply (zenon_L9_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.72/8.90 apply (zenon_L784_); trivial. % 8.72/8.90 apply (zenon_L553_); trivial. % 8.72/8.90 (* end of lemma zenon_L806_ *) % 8.72/8.90 assert (zenon_L807_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 8.72/8.90 do 0 intro. intros zenon_H2d2 zenon_Had zenon_Hc3. % 8.72/8.90 cut (((op (e1) (e2)) = (e0)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 8.72/8.90 intro zenon_D_pnotp. % 8.72/8.90 apply zenon_H2d2. % 8.72/8.90 rewrite <- zenon_D_pnotp. % 8.72/8.90 exact zenon_Had. % 8.72/8.90 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H171]. % 8.72/8.90 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 8.72/8.90 congruence. % 8.72/8.90 apply zenon_H2d. apply refl_equal. % 8.72/8.90 apply zenon_H171. apply sym_equal. exact zenon_Hc3. % 8.72/8.90 (* end of lemma zenon_L807_ *) % 8.72/8.90 assert (zenon_L808_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e3)) -> (~((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 (e2) (e0)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> False). % 8.72/8.90 do 0 intro. intros zenon_H371 zenon_Ha7 zenon_H9a zenon_H3b zenon_H29f zenon_H71 zenon_H170 zenon_H2d4 zenon_H1b1 zenon_Hc2 zenon_Had zenon_H2d2 zenon_Hc9 zenon_Hfe. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H371); [ zenon_intro zenon_H14e | zenon_intro zenon_H372 ]. % 8.72/8.90 apply (zenon_L564_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H372); [ zenon_intro zenon_H1df | zenon_intro zenon_H373 ]. % 8.72/8.90 apply (zenon_L685_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H373); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hd4 ]. % 8.72/8.90 apply (zenon_L807_); trivial. % 8.72/8.90 apply (zenon_L68_); trivial. % 8.72/8.90 (* end of lemma zenon_L808_ *) % 8.72/8.90 assert (zenon_L809_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (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)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.72/8.90 do 0 intro. intros zenon_H2e8 zenon_Ha3 zenon_Hfe zenon_Hc9 zenon_H2d2 zenon_Had zenon_Hc2 zenon_H2d4 zenon_H170 zenon_H71 zenon_H29f zenon_H9a zenon_H371 zenon_Ha8 zenon_H3b zenon_H1d9 zenon_H1b1. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2e8); [ zenon_intro zenon_H276 | zenon_intro zenon_H2e9 ]. % 8.72/8.90 apply (zenon_L245_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2e9); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H2ea ]. % 8.72/8.90 apply (zenon_L808_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_H99 | zenon_intro zenon_H98 ]. % 8.72/8.90 apply (zenon_L346_); trivial. % 8.72/8.90 apply (zenon_L375_); trivial. % 8.72/8.90 (* end of lemma zenon_L809_ *) % 8.72/8.90 assert (zenon_L810_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (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)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.72/8.90 do 0 intro. intros zenon_H2c0 zenon_H358 zenon_H27e zenon_H1dd zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H1f6 zenon_H201 zenon_Ha8 zenon_H1b1. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_Hcb | zenon_intro zenon_H2c4 ]. % 8.72/8.90 apply (zenon_L713_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H2c5 ]. % 8.72/8.90 apply (zenon_L714_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1d8 ]. % 8.72/8.90 apply (zenon_L217_); trivial. % 8.72/8.90 apply (zenon_L719_); trivial. % 8.72/8.90 (* end of lemma zenon_L810_ *) % 8.72/8.90 assert (zenon_L811_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 8.72/8.90 do 0 intro. intros zenon_H389 zenon_Ha8 zenon_H201 zenon_H1f6 zenon_H27e zenon_H2c0 zenon_H2c9 zenon_H1dd zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H1b1 zenon_Hf3. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H389); [ zenon_intro zenon_H358 | zenon_intro zenon_H38a ]. % 8.72/8.90 apply (zenon_L810_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H38a); [ zenon_intro zenon_H2a | zenon_intro zenon_H38b ]. % 8.72/8.90 apply (zenon_L307_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H38b); [ zenon_intro zenon_Hcc | zenon_intro zenon_Ha2 ]. % 8.72/8.90 apply (zenon_L714_); trivial. % 8.72/8.90 apply (zenon_L559_); trivial. % 8.72/8.90 (* end of lemma zenon_L811_ *) % 8.72/8.90 assert (zenon_L812_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (((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 (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.72/8.90 do 0 intro. intros zenon_H336 zenon_H109 zenon_H7d zenon_H3b zenon_H303 zenon_H36 zenon_H35 zenon_Hf3 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H6c zenon_H1dd zenon_H2c9 zenon_H2c0 zenon_H27e zenon_H1f6 zenon_H201 zenon_Ha8 zenon_H389 zenon_Ha3 zenon_H1b1. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.72/8.90 apply (zenon_L740_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.72/8.90 apply (zenon_L5_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.72/8.90 apply (zenon_L811_); trivial. % 8.72/8.90 apply (zenon_L553_); trivial. % 8.72/8.90 (* end of lemma zenon_L812_ *) % 8.72/8.90 assert (zenon_L813_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (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) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.72/8.90 do 0 intro. intros zenon_Hf9 zenon_H195 zenon_Hff zenon_He4 zenon_Hd0 zenon_H10f zenon_H105 zenon_H9a zenon_Ha8 zenon_H1b1 zenon_H7d zenon_H322 zenon_H1dd zenon_H6b zenon_Ha7 zenon_H134 zenon_H3b zenon_H90 zenon_H29f zenon_H1e zenon_H25 zenon_H300 zenon_H16d zenon_H35. % 8.72/8.90 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hfc ]. % 8.72/8.90 apply (zenon_L766_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hfd ]. % 8.72/8.90 apply (zenon_L313_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_Hf6 | zenon_intro zenon_He5 ]. % 8.72/8.90 apply (zenon_L734_); trivial. % 8.72/8.90 apply (zenon_L267_); trivial. % 8.72/8.90 (* end of lemma zenon_L813_ *) % 8.72/8.90 assert (zenon_L814_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((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)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> False). % 8.72/8.90 do 0 intro. intros zenon_H11f zenon_H78 zenon_H67 zenon_H35 zenon_H16d zenon_H300 zenon_H25 zenon_H1e zenon_H29f zenon_H90 zenon_H3b zenon_H134 zenon_Ha7 zenon_H6b zenon_H1dd zenon_H322 zenon_H7d zenon_H1b1 zenon_Ha8 zenon_H9a zenon_H105 zenon_Hd0 zenon_He4 zenon_Hff zenon_H195 zenon_Hf9 zenon_Hc9 zenon_Hfe. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.72/8.90 apply (zenon_L394_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.72/8.90 apply (zenon_L263_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.72/8.90 apply (zenon_L813_); trivial. % 8.72/8.90 apply (zenon_L68_); trivial. % 8.72/8.90 (* end of lemma zenon_L814_ *) % 8.72/8.90 assert (zenon_L815_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (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) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (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 (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e3))) -> False). % 8.72/8.90 do 0 intro. intros zenon_Hc5 zenon_H1d9 zenon_H371 zenon_H170 zenon_H2d4 zenon_H2d2 zenon_H36a zenon_H389 zenon_H201 zenon_H1f6 zenon_H2c0 zenon_H2c9 zenon_H6c zenon_H164 zenon_H1f zenon_H2e2 zenon_Hf3 zenon_H36 zenon_H303 zenon_H109 zenon_H336 zenon_Hcc zenon_H2e8 zenon_Ha3 zenon_H71 zenon_Hfe zenon_Hc9 zenon_Hf9 zenon_Hff zenon_He4 zenon_Hd0 zenon_H105 zenon_H9a zenon_H1b1 zenon_H7d zenon_H322 zenon_H1dd zenon_H6b zenon_H134 zenon_H90 zenon_H29f zenon_H1e zenon_H25 zenon_H300 zenon_H16d zenon_H35 zenon_H67 zenon_H78 zenon_H11f zenon_Ha8 zenon_H3b zenon_Hc2. % 8.72/8.90 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_H24 | zenon_intro zenon_Hc6 ]. % 8.72/8.90 apply (zenon_L22_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Had | zenon_intro zenon_Hc7 ]. % 8.72/8.90 apply (zenon_L809_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H80 | zenon_intro zenon_Hc3 ]. % 8.72/8.90 apply (zenon_L40_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.72/8.90 apply (zenon_L812_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.72/8.90 apply (zenon_L512_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.72/8.90 apply (zenon_L346_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2e8); [ zenon_intro zenon_H276 | zenon_intro zenon_H2e9 ]. % 8.72/8.90 apply (zenon_L245_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2e9); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H2ea ]. % 8.72/8.90 apply (zenon_L814_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2ea); [ zenon_intro zenon_H99 | zenon_intro zenon_H98 ]. % 8.72/8.90 apply (zenon_L346_); trivial. % 8.72/8.90 apply (zenon_L42_); trivial. % 8.72/8.90 (* end of lemma zenon_L815_ *) % 8.72/8.90 assert (zenon_L816_ : (~((e0) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (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) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.72/8.90 do 0 intro. intros zenon_Hc2 zenon_H3b zenon_H11f zenon_H78 zenon_H67 zenon_H35 zenon_H16d zenon_H300 zenon_H25 zenon_H1e zenon_H29f zenon_H90 zenon_H134 zenon_H6b zenon_H1dd zenon_H322 zenon_H7d zenon_H9a zenon_H105 zenon_Hd0 zenon_He4 zenon_Hff zenon_Hf9 zenon_Hc9 zenon_Hfe zenon_H71 zenon_Ha3 zenon_H2e8 zenon_H336 zenon_H109 zenon_H303 zenon_H36 zenon_Hf3 zenon_H2e2 zenon_H1f zenon_H164 zenon_H6c zenon_H2c9 zenon_H2c0 zenon_H389 zenon_H36a zenon_H2d2 zenon_H2d4 zenon_H170 zenon_H371 zenon_H1d9 zenon_Hc5 zenon_H1f6 zenon_H201 zenon_Ha8 zenon_H1b1. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_Hcb | zenon_intro zenon_H2c4 ]. % 8.72/8.90 apply (zenon_L656_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H2c5 ]. % 8.72/8.90 apply (zenon_L815_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1d8 ]. % 8.72/8.90 apply (zenon_L217_); trivial. % 8.72/8.90 apply (zenon_L719_); trivial. % 8.72/8.90 (* end of lemma zenon_L816_ *) % 8.72/8.90 assert (zenon_L817_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.72/8.90 do 0 intro. intros zenon_H36a zenon_H2c0 zenon_H1f6 zenon_H201 zenon_Ha3 zenon_H3b zenon_H371 zenon_H67 zenon_Hf0 zenon_Hc2 zenon_Had zenon_H2d2 zenon_H329 zenon_Hf3 zenon_H1b1 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H15a zenon_H6c zenon_H1dd zenon_H2c9 zenon_Hcb zenon_H389 zenon_Hb0 zenon_H145 zenon_H192 zenon_H165 zenon_H282 zenon_H7d zenon_Ha8 zenon_H105 zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.72/8.90 apply (zenon_L811_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.72/8.90 apply (zenon_L395_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.72/8.90 apply (zenon_L346_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H371); [ zenon_intro zenon_H14e | zenon_intro zenon_H372 ]. % 8.72/8.90 apply (zenon_L94_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H372); [ zenon_intro zenon_H1df | zenon_intro zenon_H373 ]. % 8.72/8.90 apply (zenon_L685_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H373); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hd4 ]. % 8.72/8.90 apply (zenon_L807_); trivial. % 8.72/8.90 apply (zenon_L730_); trivial. % 8.72/8.90 (* end of lemma zenon_L817_ *) % 8.72/8.90 assert (zenon_L818_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> False). % 8.72/8.90 do 0 intro. intros zenon_H205 zenon_H9a zenon_H3b. % 8.72/8.90 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H3c. zenon_intro zenon_H206. % 8.72/8.90 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_Hbd. zenon_intro zenon_H1ad. % 8.72/8.90 apply (zenon_L513_); trivial. % 8.72/8.90 (* end of lemma zenon_L818_ *) % 8.72/8.90 assert (zenon_L819_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 8.72/8.90 do 0 intro. intros zenon_H20d zenon_H2f3 zenon_Hd0 zenon_H16d zenon_H1f zenon_H270 zenon_H2a4 zenon_H2b5 zenon_H2b8 zenon_H2c0 zenon_H169 zenon_H1dc zenon_H2a1 zenon_H295 zenon_H19a zenon_H2c9 zenon_H145 zenon_Hb7 zenon_H6c zenon_Ha3 zenon_H74 zenon_H150 zenon_H282 zenon_H137 zenon_H173 zenon_H27f zenon_H10c zenon_H2e8 zenon_H285 zenon_Hf3 zenon_Hf9 zenon_H78 zenon_H2a2 zenon_H3a zenon_H170 zenon_H1f6 zenon_H22d zenon_Hc2 zenon_H192 zenon_H7d zenon_H2b zenon_Hab zenon_H31 zenon_H22e zenon_H129 zenon_H197 zenon_H1d7 zenon_H11f zenon_H67 zenon_H12b zenon_H124 zenon_H25 zenon_H36 zenon_Hb4 zenon_H153 zenon_H1d9 zenon_H2df zenon_Ha8 zenon_H127 zenon_H2a3 zenon_Hff zenon_H109 zenon_H2d8 zenon_Hf8 zenon_H164 zenon_H1dd zenon_H2e2 zenon_H2d2 zenon_H29f zenon_H2d4 zenon_H2a5 zenon_H2bf zenon_H1d3. % 8.72/8.90 apply (zenon_and_s _ _ zenon_H20d). zenon_intro zenon_H1a9. zenon_intro zenon_H20e. % 8.72/8.90 apply (zenon_L354_); trivial. % 8.72/8.90 (* end of lemma zenon_L819_ *) % 8.72/8.90 assert (zenon_L820_ : (((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)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((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 (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> False). % 8.72/8.90 do 0 intro. intros zenon_H322 zenon_H7d zenon_Hf0 zenon_H1b1 zenon_Ha8 zenon_H65 zenon_H2d4 zenon_Had zenon_H2d2 zenon_H71 zenon_H29f zenon_H3b zenon_H9a zenon_H59. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H323 ]. % 8.72/8.90 apply (zenon_L55_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H324 ]. % 8.72/8.90 apply (zenon_L719_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_Hbd | zenon_intro zenon_He8 ]. % 8.72/8.90 apply (zenon_L295_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H2d5 ]. % 8.72/8.90 apply (zenon_L807_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H2d6 ]. % 8.72/8.90 apply (zenon_L266_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_Hbd | zenon_intro zenon_H98 ]. % 8.72/8.90 apply (zenon_L513_); trivial. % 8.72/8.90 apply (zenon_L492_); trivial. % 8.72/8.90 (* end of lemma zenon_L820_ *) % 8.72/8.90 assert (zenon_L821_ : (((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)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.72/8.90 do 0 intro. intros zenon_H35d zenon_H78 zenon_Hb0 zenon_Hcb zenon_H27e zenon_H59 zenon_H9a zenon_H3b zenon_H29f zenon_H71 zenon_H2d2 zenon_H2d4 zenon_H65 zenon_Ha8 zenon_H1b1 zenon_Hf0 zenon_H7d zenon_H322 zenon_H67 zenon_H35. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H35d); [ zenon_intro zenon_Hac | zenon_intro zenon_H35f ]. % 8.72/8.90 apply (zenon_L305_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_H358 | zenon_intro zenon_H360 ]. % 8.72/8.90 apply (zenon_L713_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Had | zenon_intro zenon_Hd1 ]. % 8.72/8.90 apply (zenon_L820_); trivial. % 8.72/8.90 apply (zenon_L263_); trivial. % 8.72/8.90 (* end of lemma zenon_L821_ *) % 8.72/8.90 assert (zenon_L822_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((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)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.72/8.90 do 0 intro. intros zenon_H36a zenon_H2d4 zenon_H2d2 zenon_H71 zenon_H29f zenon_H59 zenon_Hcb zenon_Hb0 zenon_H78 zenon_H35d zenon_H169 zenon_H11f zenon_H31 zenon_H1e zenon_H67 zenon_H9a zenon_H3b zenon_H322 zenon_H7d zenon_Hf0 zenon_H1b1 zenon_Ha8 zenon_H65 zenon_H105 zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.72/8.90 apply (zenon_L821_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.72/8.90 apply (zenon_L432_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.72/8.90 apply (zenon_L346_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H30 | zenon_intro zenon_H122 ]. % 8.72/8.90 apply (zenon_L4_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H123 ]. % 8.72/8.90 apply (zenon_L263_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H10f | zenon_intro zenon_Hd4 ]. % 8.72/8.90 apply (zenon_L766_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H322); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H323 ]. % 8.72/8.90 apply (zenon_L55_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H324 ]. % 8.72/8.90 apply (zenon_L719_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_Hbd | zenon_intro zenon_He8 ]. % 8.72/8.90 apply (zenon_L295_); trivial. % 8.72/8.90 apply (zenon_L691_); trivial. % 8.72/8.90 (* end of lemma zenon_L822_ *) % 8.72/8.90 assert (zenon_L823_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 8.72/8.90 do 0 intro. intros zenon_H10c zenon_Hff zenon_He4 zenon_Hd0 zenon_H105 zenon_H65 zenon_Ha8 zenon_H1b1 zenon_Hf0 zenon_H322 zenon_H9a zenon_H67 zenon_H1e zenon_H31 zenon_H11f zenon_H169 zenon_H35d zenon_H78 zenon_H59 zenon_H29f zenon_H71 zenon_H2d2 zenon_H2d4 zenon_H36a zenon_Hcb zenon_H6c zenon_H94 zenon_H3b zenon_H35 zenon_H7d. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.72/8.90 apply (zenon_L822_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.72/8.90 apply (zenon_L45_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.72/8.90 apply (zenon_L28_); trivial. % 8.72/8.90 apply (zenon_L584_); trivial. % 8.72/8.90 (* end of lemma zenon_L823_ *) % 8.72/8.90 assert (zenon_L824_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (((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)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 8.72/8.90 do 0 intro. intros zenon_H11e zenon_H35 zenon_H94 zenon_H6c zenon_H36a zenon_H2d4 zenon_H2d2 zenon_H29f zenon_H59 zenon_H78 zenon_H35d zenon_H169 zenon_H11f zenon_H31 zenon_H1e zenon_H67 zenon_H65 zenon_H105 zenon_Hd0 zenon_Hff zenon_H10c zenon_H71 zenon_H322 zenon_H7d zenon_Hf0 zenon_H1b1 zenon_Ha8 zenon_H3b zenon_H9a zenon_He4. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.72/8.90 apply (zenon_L21_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.72/8.90 apply (zenon_L823_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.72/8.90 apply (zenon_L23_); trivial. % 8.72/8.90 apply (zenon_L771_); trivial. % 8.72/8.90 (* end of lemma zenon_L824_ *) % 8.72/8.90 assert (zenon_L825_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.72/8.90 do 0 intro. intros zenon_Hf9 zenon_He4 zenon_H9a zenon_H3b zenon_Ha8 zenon_H7d zenon_H322 zenon_H10c zenon_Hff zenon_Hd0 zenon_H105 zenon_H65 zenon_H67 zenon_H1e zenon_H31 zenon_H11f zenon_H169 zenon_H35d zenon_H78 zenon_H59 zenon_H2d2 zenon_H2d4 zenon_H36a zenon_H6c zenon_H94 zenon_H11e zenon_H1b1 zenon_Ha3 zenon_H71 zenon_H29f zenon_H16d zenon_H35. % 8.72/8.90 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hfc ]. % 8.72/8.90 apply (zenon_L824_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hfd ]. % 8.72/8.90 apply (zenon_L553_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_Hf6 | zenon_intro zenon_He5 ]. % 8.72/8.90 apply (zenon_L266_); trivial. % 8.72/8.90 apply (zenon_L267_); trivial. % 8.72/8.90 (* end of lemma zenon_L825_ *) % 8.72/8.90 assert (zenon_L826_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((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). % 8.72/8.90 do 0 intro. intros zenon_H2df zenon_H35 zenon_H16d zenon_H1b1 zenon_H11e zenon_H94 zenon_H6c zenon_H36a zenon_H2d4 zenon_H2d2 zenon_H59 zenon_H78 zenon_H35d zenon_H169 zenon_H11f zenon_H31 zenon_H67 zenon_H65 zenon_H105 zenon_Hd0 zenon_Hff zenon_H10c zenon_H322 zenon_Ha8 zenon_H9a zenon_He4 zenon_Hf9 zenon_Ha3 zenon_H7d zenon_H300 zenon_H25 zenon_H1e zenon_H29f zenon_H90 zenon_H3b zenon_H134 zenon_Ha7. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.72/8.90 apply (zenon_L825_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.72/8.90 apply (zenon_L733_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.72/8.90 apply (zenon_L396_); trivial. % 8.72/8.90 apply (zenon_L734_); trivial. % 8.72/8.90 (* end of lemma zenon_L826_ *) % 8.72/8.90 assert (zenon_L827_ : (((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 (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 8.72/8.90 do 0 intro. intros zenon_H2f8 zenon_Hc3 zenon_Hf6 zenon_H2df zenon_H35 zenon_H16d zenon_H1b1 zenon_H11e zenon_H94 zenon_H6c zenon_H36a zenon_H2d4 zenon_H2d2 zenon_H59 zenon_H78 zenon_H35d zenon_H169 zenon_H11f zenon_H31 zenon_H67 zenon_H65 zenon_H105 zenon_Hd0 zenon_Hff zenon_H10c zenon_H322 zenon_Ha8 zenon_H9a zenon_He4 zenon_Hf9 zenon_Ha3 zenon_H7d zenon_H300 zenon_H25 zenon_H1e zenon_H29f zenon_H90 zenon_H3b zenon_H134. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_Had | zenon_intro zenon_H2f9 ]. % 8.72/8.90 apply (zenon_L807_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H29 | zenon_intro zenon_H2fa ]. % 8.72/8.90 apply (zenon_L466_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2fa); [ zenon_intro zenon_H93 | zenon_intro zenon_Ha7 ]. % 8.72/8.90 apply (zenon_L28_); trivial. % 8.72/8.90 apply (zenon_L826_); trivial. % 8.72/8.90 (* end of lemma zenon_L827_ *) % 8.72/8.90 assert (zenon_L828_ : (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((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) (op (e3) (e0))) = (e0))) -> (~((e0) = (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) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.72/8.90 do 0 intro. intros zenon_H129 zenon_H2c0 zenon_H371 zenon_H62 zenon_Hc2 zenon_H134 zenon_H3b zenon_H90 zenon_H29f zenon_H25 zenon_H300 zenon_Ha3 zenon_Hf9 zenon_H9a zenon_H322 zenon_H10c zenon_H65 zenon_H67 zenon_H31 zenon_H11f zenon_H169 zenon_H35d zenon_H78 zenon_H59 zenon_H2d2 zenon_H2d4 zenon_H36a zenon_H94 zenon_H11e zenon_H16d zenon_H2df zenon_H2f8 zenon_H329 zenon_Hf3 zenon_H1b1 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H15a zenon_H6c zenon_H1dd zenon_H2c9 zenon_Hcb zenon_H389 zenon_Hb0 zenon_H145 zenon_H192 zenon_H165 zenon_H282 zenon_H7d zenon_Ha8 zenon_H105 zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.72/8.90 apply (zenon_L825_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.72/8.90 apply (zenon_L74_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.72/8.90 apply (zenon_L396_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.72/8.90 apply (zenon_L739_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.72/8.90 apply (zenon_L395_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.72/8.90 apply (zenon_L346_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H371); [ zenon_intro zenon_H14e | zenon_intro zenon_H372 ]. % 8.72/8.90 apply (zenon_L416_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H372); [ zenon_intro zenon_H1df | zenon_intro zenon_H373 ]. % 8.72/8.90 apply (zenon_L685_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_H373); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hd4 ]. % 8.72/8.90 apply (zenon_L827_); trivial. % 8.72/8.90 apply (zenon_L730_); trivial. % 8.72/8.90 (* end of lemma zenon_L828_ *) % 8.72/8.90 assert (zenon_L829_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.72/8.90 do 0 intro. intros zenon_Hf9 zenon_H9a zenon_H3b zenon_H2d2 zenon_Had zenon_H2d4 zenon_H65 zenon_Ha8 zenon_H7d zenon_H322 zenon_Ha3 zenon_H71 zenon_H29f zenon_H59 zenon_H1b1. % 8.72/8.90 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hfc ]. % 8.72/8.90 apply (zenon_L820_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hfd ]. % 8.72/8.90 apply (zenon_L553_); trivial. % 8.72/8.90 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_Hf6 | zenon_intro zenon_He5 ]. % 8.72/8.90 apply (zenon_L266_); trivial. % 8.72/8.90 apply (zenon_L479_); trivial. % 8.72/8.90 (* end of lemma zenon_L829_ *) % 8.72/8.90 assert (zenon_L830_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 8.76/8.91 do 0 intro. intros zenon_H282 zenon_H10f zenon_H12b zenon_Hd4 zenon_Hfe zenon_H145 zenon_Hb0 zenon_Hcb zenon_H358. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H143 | zenon_intro zenon_H283 ]. % 8.76/8.91 apply (zenon_L253_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H284 ]. % 8.76/8.91 apply (zenon_L68_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H27e ]. % 8.76/8.91 apply (zenon_L84_); trivial. % 8.76/8.91 apply (zenon_L713_); trivial. % 8.76/8.91 (* end of lemma zenon_L830_ *) % 8.76/8.91 assert (zenon_L831_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.76/8.91 do 0 intro. intros zenon_H329 zenon_H358 zenon_Hcb zenon_Hb0 zenon_H145 zenon_H12b zenon_H10f zenon_H282 zenon_H7d zenon_Ha8 zenon_H105 zenon_Hd4 zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff zenon_H195. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hfe | zenon_intro zenon_H32a ]. % 8.76/8.91 apply (zenon_L830_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H108 | zenon_intro zenon_H32b ]. % 8.76/8.91 apply (zenon_L584_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H3c | zenon_intro zenon_He8 ]. % 8.76/8.91 apply (zenon_L368_); trivial. % 8.76/8.91 apply (zenon_L691_); trivial. % 8.76/8.91 (* end of lemma zenon_L831_ *) % 8.76/8.91 assert (zenon_L832_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((e0) = (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) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e2)) = (e1)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 8.76/8.91 do 0 intro. intros zenon_H371 zenon_H62 zenon_Hc2 zenon_H134 zenon_H3b zenon_H90 zenon_H29f zenon_H1e zenon_H25 zenon_H300 zenon_Ha3 zenon_Hf9 zenon_H9a zenon_H322 zenon_H10c zenon_H65 zenon_H67 zenon_H31 zenon_H11f zenon_H169 zenon_H35d zenon_H78 zenon_H59 zenon_H2d2 zenon_H2d4 zenon_H36a zenon_H6c zenon_H94 zenon_H11e zenon_H1b1 zenon_H16d zenon_H2df zenon_Hf6 zenon_H2f8 zenon_H329 zenon_H358 zenon_Hcb zenon_Hb0 zenon_H145 zenon_H12b zenon_H10f zenon_H282 zenon_H7d zenon_Ha8 zenon_H105 zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff zenon_H195. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H371); [ zenon_intro zenon_H14e | zenon_intro zenon_H372 ]. % 8.76/8.91 apply (zenon_L416_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H372); [ zenon_intro zenon_H1df | zenon_intro zenon_H373 ]. % 8.76/8.91 apply (zenon_L685_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H373); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hd4 ]. % 8.76/8.91 apply (zenon_L827_); trivial. % 8.76/8.91 apply (zenon_L831_); trivial. % 8.76/8.91 (* end of lemma zenon_L832_ *) % 8.76/8.91 assert (zenon_L833_ : ((op (e1) (e2)) = (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) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (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) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((e0) = (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) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.76/8.91 do 0 intro. intros zenon_Had zenon_Hf3 zenon_H2e2 zenon_H1f zenon_H164 zenon_H15a zenon_H1dd zenon_H2c9 zenon_H389 zenon_H66 zenon_H371 zenon_H62 zenon_Hc2 zenon_H134 zenon_H3b zenon_H90 zenon_H29f zenon_H1e zenon_H25 zenon_H300 zenon_Ha3 zenon_Hf9 zenon_H9a zenon_H322 zenon_H10c zenon_H65 zenon_H67 zenon_H31 zenon_H11f zenon_H169 zenon_H35d zenon_H78 zenon_H59 zenon_H2d2 zenon_H2d4 zenon_H36a zenon_H6c zenon_H94 zenon_H11e zenon_H1b1 zenon_H16d zenon_H2df zenon_H2f8 zenon_H329 zenon_H358 zenon_Hcb zenon_Hb0 zenon_H145 zenon_H12b zenon_H10f zenon_H282 zenon_H7d zenon_Ha8 zenon_H105 zenon_Hd0 zenon_H35 zenon_He4 zenon_Hff. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.76/8.91 apply (zenon_L829_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.76/8.91 apply (zenon_L110_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.76/8.91 apply (zenon_L396_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.76/8.91 apply (zenon_L715_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.76/8.91 apply (zenon_L258_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.76/8.91 apply (zenon_L346_); trivial. % 8.76/8.91 apply (zenon_L832_); trivial. % 8.76/8.91 (* end of lemma zenon_L833_ *) % 8.76/8.91 assert (zenon_L834_ : (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 8.76/8.91 do 0 intro. intros zenon_H129 zenon_H2f8 zenon_Hc3 zenon_H2df zenon_H35 zenon_H16d zenon_H1b1 zenon_H11e zenon_H94 zenon_H6c zenon_H36a zenon_H2d4 zenon_H2d2 zenon_H59 zenon_H78 zenon_H35d zenon_H169 zenon_H11f zenon_H31 zenon_H67 zenon_H65 zenon_H105 zenon_Hd0 zenon_Hff zenon_H10c zenon_H322 zenon_Ha8 zenon_H9a zenon_He4 zenon_Hf9 zenon_Ha3 zenon_H7d zenon_H300 zenon_H25 zenon_H1e zenon_H29f zenon_H90 zenon_H3b zenon_H134. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.76/8.91 apply (zenon_L825_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.76/8.91 apply (zenon_L74_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.76/8.91 apply (zenon_L396_); trivial. % 8.76/8.91 apply (zenon_L827_); trivial. % 8.76/8.91 (* end of lemma zenon_L834_ *) % 8.76/8.91 assert (zenon_L835_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> False). % 8.76/8.91 do 0 intro. intros zenon_H371 zenon_H62 zenon_H1b1 zenon_Hc2 zenon_Had zenon_H2d2 zenon_Hc9 zenon_Hfe. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H371); [ zenon_intro zenon_H14e | zenon_intro zenon_H372 ]. % 8.76/8.91 apply (zenon_L416_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H372); [ zenon_intro zenon_H1df | zenon_intro zenon_H373 ]. % 8.76/8.91 apply (zenon_L685_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H373); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hd4 ]. % 8.76/8.91 apply (zenon_L807_); trivial. % 8.76/8.91 apply (zenon_L68_); trivial. % 8.76/8.91 (* end of lemma zenon_L835_ *) % 8.76/8.91 assert (zenon_L836_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.76/8.91 do 0 intro. intros zenon_H303 zenon_Hfe zenon_H2d2 zenon_Had zenon_Hc2 zenon_H1b1 zenon_H62 zenon_H371 zenon_H164 zenon_H6b zenon_H3b zenon_H7d zenon_H109 zenon_H35. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.76/8.91 apply (zenon_L835_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.76/8.91 apply (zenon_L534_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.76/8.91 apply (zenon_L396_); trivial. % 8.76/8.91 apply (zenon_L106_); trivial. % 8.76/8.91 (* end of lemma zenon_L836_ *) % 8.76/8.91 assert (zenon_L837_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 8.76/8.91 do 0 intro. intros zenon_Hc5 zenon_H109 zenon_H6b zenon_H164 zenon_H371 zenon_H62 zenon_Hc2 zenon_Hfe zenon_H303 zenon_H129 zenon_H2f8 zenon_H2df zenon_H35 zenon_H16d zenon_H1b1 zenon_H11e zenon_H94 zenon_H6c zenon_H36a zenon_H2d4 zenon_H2d2 zenon_H59 zenon_H78 zenon_H35d zenon_H169 zenon_H11f zenon_H31 zenon_H67 zenon_H65 zenon_H105 zenon_Hd0 zenon_Hff zenon_H10c zenon_H322 zenon_Ha8 zenon_H9a zenon_He4 zenon_Hf9 zenon_Ha3 zenon_H7d zenon_H300 zenon_H25 zenon_H1e zenon_H29f zenon_H90 zenon_H3b zenon_H134. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_H24 | zenon_intro zenon_Hc6 ]. % 8.76/8.91 apply (zenon_L2_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Had | zenon_intro zenon_Hc7 ]. % 8.76/8.91 apply (zenon_L836_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H80 | zenon_intro zenon_Hc3 ]. % 8.76/8.91 apply (zenon_L40_); trivial. % 8.76/8.91 apply (zenon_L834_); trivial. % 8.76/8.91 (* end of lemma zenon_L837_ *) % 8.76/8.91 assert (zenon_L838_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 8.76/8.91 do 0 intro. intros zenon_Hc5 zenon_H109 zenon_H6b zenon_H164 zenon_H371 zenon_H62 zenon_Hc2 zenon_H303 zenon_H129 zenon_H2f8 zenon_H2df zenon_H35 zenon_H16d zenon_H1b1 zenon_H11e zenon_H94 zenon_H6c zenon_H36a zenon_H2d4 zenon_H2d2 zenon_H59 zenon_H78 zenon_H35d zenon_H169 zenon_H11f zenon_H31 zenon_H67 zenon_H65 zenon_H105 zenon_Hd0 zenon_Hff zenon_H10c zenon_H322 zenon_Ha8 zenon_H9a zenon_He4 zenon_Hf9 zenon_Ha3 zenon_H7d zenon_H300 zenon_H25 zenon_H1e zenon_H29f zenon_H90 zenon_H3b zenon_H134. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.76/8.91 apply (zenon_L21_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.76/8.91 apply (zenon_L656_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.76/8.91 apply (zenon_L565_); trivial. % 8.76/8.91 apply (zenon_L837_); trivial. % 8.76/8.91 (* end of lemma zenon_L838_ *) % 8.76/8.91 assert (zenon_L839_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (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)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (((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) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 8.76/8.91 do 0 intro. intros zenon_Hff zenon_He4 zenon_Hd0 zenon_H105 zenon_Ha8 zenon_H282 zenon_H165 zenon_H192 zenon_H145 zenon_H389 zenon_Hcb zenon_H2c9 zenon_Hf3 zenon_H329 zenon_H2f8 zenon_H2df zenon_H16d zenon_H11e zenon_H36a zenon_H2d4 zenon_H2d2 zenon_H59 zenon_H78 zenon_H35d zenon_H169 zenon_H11f zenon_H31 zenon_H67 zenon_H65 zenon_H10c zenon_H322 zenon_H9a zenon_Hf9 zenon_Ha3 zenon_H300 zenon_H25 zenon_H29f zenon_H90 zenon_H134 zenon_Hc2 zenon_H62 zenon_H371 zenon_H2c0 zenon_H129 zenon_H1dd zenon_H1b1 zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H94 zenon_H3b zenon_H35 zenon_H7d. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.76/8.91 apply (zenon_L828_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.76/8.91 apply (zenon_L714_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.76/8.91 apply (zenon_L28_); trivial. % 8.76/8.91 apply (zenon_L584_); trivial. % 8.76/8.91 (* end of lemma zenon_L839_ *) % 8.76/8.91 assert (zenon_L840_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (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 (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (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) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (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) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> False). % 8.76/8.91 do 0 intro. intros zenon_H336 zenon_H303 zenon_H109 zenon_Hc5 zenon_H36 zenon_H7d zenon_H35 zenon_H3b zenon_H94 zenon_H6c zenon_Hcb zenon_H285 zenon_H137 zenon_H129 zenon_H2c0 zenon_H192 zenon_Had zenon_Hf3 zenon_H2e2 zenon_H1f zenon_H164 zenon_H1dd zenon_H2c9 zenon_H389 zenon_H66 zenon_H371 zenon_H62 zenon_Hc2 zenon_H134 zenon_H90 zenon_H29f zenon_H1e zenon_H25 zenon_H300 zenon_Ha3 zenon_Hf9 zenon_H9a zenon_H322 zenon_H10c zenon_H65 zenon_H67 zenon_H31 zenon_H11f zenon_H169 zenon_H35d zenon_H78 zenon_H59 zenon_H2d2 zenon_H2d4 zenon_H36a zenon_H11e zenon_H1b1 zenon_H16d zenon_H2df zenon_H2f8 zenon_H329 zenon_H358 zenon_H145 zenon_H12b zenon_H282 zenon_Ha8 zenon_H105 zenon_Hd0 zenon_He4 zenon_Hff zenon_H64. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.91 apply (zenon_L838_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.91 apply (zenon_L5_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H143 | zenon_intro zenon_H286 ]. % 8.76/8.91 apply (zenon_L673_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H165 | zenon_intro zenon_H287 ]. % 8.76/8.91 apply (zenon_L839_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H80 | zenon_intro zenon_H10f ]. % 8.76/8.91 apply (zenon_L40_); trivial. % 8.76/8.91 apply (zenon_L833_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.76/8.91 apply (zenon_L45_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.76/8.91 apply (zenon_L28_); trivial. % 8.76/8.91 apply (zenon_L584_); trivial. % 8.76/8.91 apply (zenon_L265_); trivial. % 8.76/8.91 (* end of lemma zenon_L840_ *) % 8.76/8.91 assert (zenon_L841_ : ((op (e1) (e2)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((e0) = (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) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 8.76/8.91 do 0 intro. intros zenon_Had zenon_H371 zenon_H62 zenon_Hc2 zenon_H134 zenon_H3b zenon_H90 zenon_H29f zenon_H25 zenon_H300 zenon_H7d zenon_Ha3 zenon_Hf9 zenon_He4 zenon_H9a zenon_Ha8 zenon_H322 zenon_H10c zenon_Hff zenon_Hd0 zenon_H105 zenon_H65 zenon_H67 zenon_H31 zenon_H11f zenon_H169 zenon_H35d zenon_H78 zenon_H59 zenon_H2d2 zenon_H2d4 zenon_H36a zenon_H94 zenon_H11e zenon_H16d zenon_H35 zenon_H2df zenon_H2f8 zenon_H282 zenon_H165 zenon_H192 zenon_Hfe zenon_H145 zenon_Hb0 zenon_H389 zenon_Hcb zenon_H2c9 zenon_H1dd zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H1b1 zenon_Hf3. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.76/8.91 apply (zenon_L829_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.76/8.91 apply (zenon_L110_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.76/8.91 apply (zenon_L396_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H371); [ zenon_intro zenon_H14e | zenon_intro zenon_H372 ]. % 8.76/8.91 apply (zenon_L416_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H372); [ zenon_intro zenon_H1df | zenon_intro zenon_H373 ]. % 8.76/8.91 apply (zenon_L685_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H373); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hd4 ]. % 8.76/8.91 apply (zenon_L827_); trivial. % 8.76/8.91 apply (zenon_L729_); trivial. % 8.76/8.91 (* end of lemma zenon_L841_ *) % 8.76/8.91 assert (zenon_L842_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.76/8.91 do 0 intro. intros zenon_H2c0 zenon_Hf3 zenon_H2c9 zenon_H389 zenon_Hb0 zenon_H145 zenon_Hfe zenon_H192 zenon_H165 zenon_H282 zenon_H2f8 zenon_H2df zenon_H35 zenon_H16d zenon_H11e zenon_H94 zenon_H36a zenon_H2d4 zenon_H2d2 zenon_H59 zenon_H78 zenon_H35d zenon_H169 zenon_H11f zenon_H31 zenon_H67 zenon_H65 zenon_H105 zenon_Hd0 zenon_Hff zenon_H10c zenon_H322 zenon_H9a zenon_He4 zenon_Hf9 zenon_Ha3 zenon_H300 zenon_H25 zenon_H29f zenon_H90 zenon_H3b zenon_H134 zenon_Hc2 zenon_H62 zenon_H371 zenon_Had zenon_H1dd zenon_H6c zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H15a zenon_H7d zenon_Ha8 zenon_H1b1. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_Hcb | zenon_intro zenon_H2c4 ]. % 8.76/8.91 apply (zenon_L841_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H2c5 ]. % 8.76/8.91 apply (zenon_L714_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1d8 ]. % 8.76/8.91 apply (zenon_L149_); trivial. % 8.76/8.91 apply (zenon_L719_); trivial. % 8.76/8.91 (* end of lemma zenon_L842_ *) % 8.76/8.91 assert (zenon_L843_ : (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 8.76/8.91 do 0 intro. intros zenon_Ha8 zenon_H7d zenon_Had zenon_H371 zenon_H62 zenon_Hc2 zenon_H134 zenon_H90 zenon_H29f zenon_H25 zenon_H300 zenon_Ha3 zenon_Hf9 zenon_He4 zenon_H9a zenon_H322 zenon_H10c zenon_Hff zenon_H105 zenon_H65 zenon_H67 zenon_H31 zenon_H11f zenon_H169 zenon_H35d zenon_H78 zenon_H59 zenon_H2d2 zenon_H2d4 zenon_H36a zenon_H11e zenon_H16d zenon_H35 zenon_H2df zenon_H2f8 zenon_H282 zenon_H165 zenon_H192 zenon_H145 zenon_H389 zenon_H2c9 zenon_Hf3 zenon_H2c0 zenon_H1dd zenon_H1b1 zenon_H6c zenon_H15a zenon_H164 zenon_H1e zenon_H1f zenon_H2e2 zenon_H94 zenon_H3b zenon_Hd0 zenon_Hfe. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.76/8.91 apply (zenon_L842_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.76/8.91 apply (zenon_L714_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.76/8.91 apply (zenon_L28_); trivial. % 8.76/8.91 apply (zenon_L88_); trivial. % 8.76/8.91 (* end of lemma zenon_L843_ *) % 8.76/8.91 assert (zenon_L844_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (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)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e0)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> False). % 8.76/8.91 do 0 intro. intros zenon_H336 zenon_H109 zenon_H303 zenon_H36 zenon_Hfe zenon_Hd0 zenon_H3b zenon_H94 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H6c zenon_H1b1 zenon_H1dd zenon_H2c0 zenon_Hf3 zenon_H2c9 zenon_H389 zenon_H145 zenon_H192 zenon_H165 zenon_H282 zenon_H2f8 zenon_H2df zenon_H35 zenon_H16d zenon_H11e zenon_H36a zenon_H2d4 zenon_H2d2 zenon_H59 zenon_H78 zenon_H35d zenon_H169 zenon_H11f zenon_H31 zenon_H67 zenon_H65 zenon_H105 zenon_Hff zenon_H10c zenon_H322 zenon_H9a zenon_He4 zenon_Hf9 zenon_Ha3 zenon_H300 zenon_H25 zenon_H29f zenon_H90 zenon_H134 zenon_Hc2 zenon_H62 zenon_H371 zenon_Had zenon_H7d zenon_Ha8 zenon_H64. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.91 apply (zenon_L836_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.91 apply (zenon_L5_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.91 apply (zenon_L843_); trivial. % 8.76/8.91 apply (zenon_L265_); trivial. % 8.76/8.91 (* end of lemma zenon_L844_ *) % 8.76/8.91 assert (zenon_L845_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (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 (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 8.76/8.91 do 0 intro. intros zenon_Hc5 zenon_H64 zenon_H371 zenon_H62 zenon_Hc2 zenon_H282 zenon_H165 zenon_H192 zenon_H145 zenon_H389 zenon_H2c9 zenon_Hf3 zenon_H2c0 zenon_H1dd zenon_H164 zenon_H1f zenon_H2e2 zenon_Hfe zenon_H36 zenon_H303 zenon_H109 zenon_H336 zenon_H129 zenon_H2f8 zenon_H2df zenon_H35 zenon_H16d zenon_H1b1 zenon_H11e zenon_H94 zenon_H6c zenon_H36a zenon_H2d4 zenon_H2d2 zenon_H59 zenon_H78 zenon_H35d zenon_H169 zenon_H11f zenon_H31 zenon_H67 zenon_H65 zenon_H105 zenon_Hd0 zenon_Hff zenon_H10c zenon_H322 zenon_Ha8 zenon_H9a zenon_He4 zenon_Hf9 zenon_Ha3 zenon_H7d zenon_H300 zenon_H25 zenon_H1e zenon_H29f zenon_H90 zenon_H3b zenon_H134. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_H24 | zenon_intro zenon_Hc6 ]. % 8.76/8.91 apply (zenon_L2_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Had | zenon_intro zenon_Hc7 ]. % 8.76/8.91 apply (zenon_L844_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H80 | zenon_intro zenon_Hc3 ]. % 8.76/8.91 apply (zenon_L40_); trivial. % 8.76/8.91 apply (zenon_L834_); trivial. % 8.76/8.91 (* end of lemma zenon_L845_ *) % 8.76/8.91 assert (zenon_L846_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((e0) = (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) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e2)) = (e1)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 8.76/8.91 do 0 intro. intros zenon_H371 zenon_H62 zenon_Hc2 zenon_H134 zenon_H3b zenon_H90 zenon_H29f zenon_H1e zenon_H25 zenon_H300 zenon_H7d zenon_Ha3 zenon_Hf9 zenon_He4 zenon_H9a zenon_Ha8 zenon_H322 zenon_H10c zenon_Hff zenon_Hd0 zenon_H105 zenon_H65 zenon_H67 zenon_H31 zenon_H11f zenon_H169 zenon_H35d zenon_H78 zenon_H59 zenon_H2d2 zenon_H2d4 zenon_H36a zenon_H6c zenon_H94 zenon_H11e zenon_H1b1 zenon_H16d zenon_H35 zenon_H2df zenon_Hf6 zenon_H2f8 zenon_H282 zenon_H10f zenon_H12b zenon_Hfe zenon_H145 zenon_Hb0 zenon_Hcb zenon_H358. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H371); [ zenon_intro zenon_H14e | zenon_intro zenon_H372 ]. % 8.76/8.91 apply (zenon_L416_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H372); [ zenon_intro zenon_H1df | zenon_intro zenon_H373 ]. % 8.76/8.91 apply (zenon_L685_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H373); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hd4 ]. % 8.76/8.91 apply (zenon_L827_); trivial. % 8.76/8.91 apply (zenon_L830_); trivial. % 8.76/8.91 (* end of lemma zenon_L846_ *) % 8.76/8.91 assert (zenon_L847_ : ((op (e1) (e2)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((e0) = (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) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 8.76/8.91 do 0 intro. intros zenon_Had zenon_H371 zenon_H62 zenon_Hc2 zenon_H134 zenon_H3b zenon_H90 zenon_H29f zenon_H1e zenon_H25 zenon_H300 zenon_H7d zenon_Ha3 zenon_Hf9 zenon_He4 zenon_H9a zenon_Ha8 zenon_H322 zenon_H10c zenon_Hff zenon_Hd0 zenon_H105 zenon_H65 zenon_H67 zenon_H31 zenon_H11f zenon_H169 zenon_H35d zenon_H78 zenon_H59 zenon_H2d2 zenon_H2d4 zenon_H36a zenon_H6c zenon_H94 zenon_H11e zenon_H1b1 zenon_H16d zenon_H35 zenon_H2df zenon_H2f8 zenon_H282 zenon_H10f zenon_H12b zenon_Hfe zenon_H145 zenon_Hb0 zenon_Hcb zenon_H358. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H71 | zenon_intro zenon_H2e0 ]. % 8.76/8.91 apply (zenon_L829_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H29 | zenon_intro zenon_H2e1 ]. % 8.76/8.91 apply (zenon_L110_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H91 | zenon_intro zenon_Hf6 ]. % 8.76/8.91 apply (zenon_L396_); trivial. % 8.76/8.91 apply (zenon_L846_); trivial. % 8.76/8.91 (* end of lemma zenon_L847_ *) % 8.76/8.91 assert (zenon_L848_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 8.76/8.91 do 0 intro. intros zenon_Hc5 zenon_H358 zenon_Hcb zenon_Hb0 zenon_H145 zenon_Hfe zenon_H12b zenon_H10f zenon_H282 zenon_Hc2 zenon_H62 zenon_H371 zenon_H129 zenon_H2f8 zenon_H2df zenon_H35 zenon_H16d zenon_H1b1 zenon_H11e zenon_H94 zenon_H6c zenon_H36a zenon_H2d4 zenon_H2d2 zenon_H59 zenon_H78 zenon_H35d zenon_H169 zenon_H11f zenon_H31 zenon_H67 zenon_H65 zenon_H105 zenon_Hd0 zenon_Hff zenon_H10c zenon_H322 zenon_Ha8 zenon_H9a zenon_He4 zenon_Hf9 zenon_Ha3 zenon_H7d zenon_H300 zenon_H25 zenon_H1e zenon_H29f zenon_H90 zenon_H3b zenon_H134. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_H24 | zenon_intro zenon_Hc6 ]. % 8.76/8.91 apply (zenon_L2_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Had | zenon_intro zenon_Hc7 ]. % 8.76/8.91 apply (zenon_L847_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H80 | zenon_intro zenon_Hc3 ]. % 8.76/8.91 apply (zenon_L40_); trivial. % 8.76/8.91 apply (zenon_L834_); trivial. % 8.76/8.91 (* end of lemma zenon_L848_ *) % 8.76/8.91 assert (zenon_L849_ : (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (op (e3) (e2))) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e3) (e0))) = (e0))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (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 (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e3) (op (e3) (e1))) = (e1))) -> False). % 8.76/8.91 do 0 intro. intros zenon_H7d zenon_H35 zenon_H3b zenon_H94 zenon_H2e2 zenon_H1f zenon_H1e zenon_H164 zenon_H6c zenon_H1b1 zenon_H1dd zenon_H134 zenon_H90 zenon_H29f zenon_H25 zenon_H300 zenon_Ha3 zenon_Hf9 zenon_He4 zenon_H9a zenon_H322 zenon_H10c zenon_Hff zenon_Hd0 zenon_H105 zenon_H65 zenon_H67 zenon_H31 zenon_H11f zenon_H169 zenon_H35d zenon_H78 zenon_H59 zenon_H2d2 zenon_H2d4 zenon_H36a zenon_H11e zenon_H16d zenon_H2df zenon_H2f8 zenon_H129 zenon_H371 zenon_H62 zenon_Hc2 zenon_H282 zenon_H12b zenon_Hfe zenon_H145 zenon_H358 zenon_Hc5 zenon_H192 zenon_H389 zenon_H2c9 zenon_Hf3 zenon_H2c0 zenon_H36 zenon_H303 zenon_H109 zenon_H336 zenon_H137 zenon_H285 zenon_Ha8 zenon_H64. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.91 apply (zenon_L837_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.91 apply (zenon_L5_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_Hcb | zenon_intro zenon_H2c4 ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H143 | zenon_intro zenon_H286 ]. % 8.76/8.91 apply (zenon_L673_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H165 | zenon_intro zenon_H287 ]. % 8.76/8.91 apply (zenon_L845_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H80 | zenon_intro zenon_H10f ]. % 8.76/8.91 apply (zenon_L40_); trivial. % 8.76/8.91 apply (zenon_L848_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H2c5 ]. % 8.76/8.91 apply (zenon_L714_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1d8 ]. % 8.76/8.91 apply (zenon_L149_); trivial. % 8.76/8.91 apply (zenon_L719_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.76/8.91 apply (zenon_L714_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.76/8.91 apply (zenon_L28_); trivial. % 8.76/8.91 apply (zenon_L584_); trivial. % 8.76/8.91 apply (zenon_L265_); trivial. % 8.76/8.91 (* end of lemma zenon_L849_ *) % 8.76/8.91 assert (zenon_L850_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e0) (e0)) = (e0))/\((op (e0) (e0)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e1) (e0)) = (e0))/\((op (e0) (e1)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e2) (e0)) = (e0))/\((op (e0) (e2)) = (e0)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((op (e3) (e0)) = (e0))/\((op (e0) (e3)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e0) (e1)) = (e1))/\((op (e1) (e0)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e1) (e1)) = (e1))/\((op (e1) (e1)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e2) (e1)) = (e1))/\((op (e1) (e2)) = (e1)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((op (e3) (e1)) = (e1))/\((op (e1) (e3)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e0) (e2)) = (e2))/\((op (e2) (e0)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e1) (e2)) = (e2))/\((op (e2) (e1)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e2) (e2)) = (e2))/\((op (e2) (e2)) = (e2)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((op (e3) (e2)) = (e2))/\((op (e2) (e3)) = (e2)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e0) (e3)) = (e3))/\((op (e3) (e0)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e1) (e3)) = (e3))/\((op (e3) (e1)) = (e3)))))\/((((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e2) (e3)) = (e3))/\((op (e3) (e2)) = (e3)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((~((op (e0) (op (e0) (e0))) = (e0)))/\((~((op (e0) (op (e0) (e1))) = (e1)))/\((~((op (e0) (op (e0) (e2))) = (e2)))/\(~((op (e0) (op (e0) (e3))) = (e3))))))\/(((~((op (e1) (op (e1) (e0))) = (e0)))/\((~((op (e1) (op (e1) (e1))) = (e1)))/\((~((op (e1) (op (e1) (e2))) = (e2)))/\(~((op (e1) (op (e1) (e3))) = (e3))))))\/(((~((op (e2) (op (e2) (e0))) = (e0)))/\((~((op (e2) (op (e2) (e1))) = (e1)))/\((~((op (e2) (op (e2) (e2))) = (e2)))/\(~((op (e2) (op (e2) (e3))) = (e3))))))\/((~((op (e3) (op (e3) (e0))) = (e0)))/\((~((op (e3) (op (e3) (e1))) = (e1)))/\((~((op (e3) (op (e3) (e2))) = (e2)))/\(~((op (e3) (op (e3) (e3))) = (e3))))))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.76/8.91 do 0 intro. intros zenon_H2fc zenon_H3a zenon_H1d7 zenon_H2f3 zenon_H270 zenon_H2a4 zenon_H2b5 zenon_H2b8 zenon_H1dc zenon_H295 zenon_H19a zenon_Hb7 zenon_H74 zenon_H150 zenon_H173 zenon_H27f zenon_H2e8 zenon_H2a2 zenon_H170 zenon_H1f6 zenon_H22d zenon_H2b zenon_Hab zenon_H22e zenon_H197 zenon_H124 zenon_Hb4 zenon_H153 zenon_H127 zenon_H2a3 zenon_H2d8 zenon_Hf8 zenon_H2a5 zenon_H2bf zenon_H1d3 zenon_Hed zenon_He7 zenon_Heb zenon_Hbf zenon_H34d zenon_Hba zenon_H32e zenon_H331 zenon_H2a1 zenon_H282 zenon_H192 zenon_H145 zenon_H389 zenon_H2c9 zenon_Hf3 zenon_H2c0 zenon_H1dd zenon_H1f zenon_H2e2 zenon_H36 zenon_H336 zenon_H12b zenon_H137 zenon_H285 zenon_H35e zenon_H329 zenon_H134 zenon_H90 zenon_H25 zenon_H300 zenon_H2df zenon_H2f8 zenon_H129 zenon_H303 zenon_Hc2 zenon_H371 zenon_H164 zenon_H109 zenon_Hc5 zenon_H16d zenon_H29f zenon_Ha3 zenon_H11e zenon_H94 zenon_H6c zenon_H36a zenon_H2d4 zenon_H2d2 zenon_H78 zenon_H35d zenon_H169 zenon_H11f zenon_H31 zenon_H1e zenon_H67 zenon_H105 zenon_Hff zenon_H10c zenon_H322 zenon_H7d zenon_Ha8 zenon_H9a zenon_He4 zenon_Hf9 zenon_Hd0 zenon_H1d9 zenon_H1b1. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c1 ]. % 8.76/8.91 apply (zenon_L2_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H29 | zenon_intro zenon_H2c2 ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.76/8.91 apply (zenon_L4_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.76/8.91 apply (zenon_L74_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.76/8.91 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.76/8.91 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 8.76/8.91 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H118. zenon_intro zenon_H18a. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.91 apply (zenon_L527_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.91 apply (zenon_L3_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.91 apply (zenon_L718_); trivial. % 8.76/8.91 apply (zenon_L553_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.76/8.91 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 8.76/8.91 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H41. zenon_intro zenon_H4a. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.91 apply (zenon_L720_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.91 apply (zenon_L9_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2c0); [ zenon_intro zenon_Hcb | zenon_intro zenon_H2c4 ]. % 8.76/8.91 apply (zenon_L716_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2c4); [ zenon_intro zenon_Hcc | zenon_intro zenon_H2c5 ]. % 8.76/8.91 apply (zenon_L85_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1d8 ]. % 8.76/8.91 apply (zenon_L149_); trivial. % 8.76/8.91 apply (zenon_L719_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.76/8.91 apply (zenon_L714_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.76/8.91 apply (zenon_L161_); trivial. % 8.76/8.91 apply (zenon_L63_); trivial. % 8.76/8.91 apply (zenon_L553_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.76/8.91 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 8.76/8.91 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 8.76/8.91 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H4c. zenon_intro zenon_H57. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H304 ]. % 8.76/8.91 apply (zenon_L721_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H15a | zenon_intro zenon_H305 ]. % 8.76/8.91 apply (zenon_L99_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H91 | zenon_intro zenon_H16b ]. % 8.76/8.91 apply (zenon_L104_); trivial. % 8.76/8.91 apply (zenon_L561_); trivial. % 8.76/8.91 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 8.76/8.91 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 8.76/8.91 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H59. % 8.76/8.91 apply (zenon_L723_); trivial. % 8.76/8.91 apply (zenon_L384_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2c2); [ zenon_intro zenon_H3b | zenon_intro zenon_H98 ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.76/8.91 apply (zenon_L4_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.76/8.91 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.76/8.91 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 8.76/8.91 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H118. zenon_intro zenon_H18a. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.76/8.91 apply (zenon_L21_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.76/8.91 apply (zenon_L21_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H35d); [ zenon_intro zenon_Hac | zenon_intro zenon_H35f ]. % 8.76/8.91 apply (zenon_L305_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_H358 | zenon_intro zenon_H360 ]. % 8.76/8.91 apply (zenon_L737_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Had | zenon_intro zenon_Hd1 ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.76/8.91 apply (zenon_L76_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.76/8.91 apply (zenon_L737_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.76/8.91 apply (zenon_L748_); trivial. % 8.76/8.91 apply (zenon_L685_); trivial. % 8.76/8.91 apply (zenon_L263_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.76/8.91 apply (zenon_L495_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H35d); [ zenon_intro zenon_Hac | zenon_intro zenon_H35f ]. % 8.76/8.91 apply (zenon_L749_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_H358 | zenon_intro zenon_H360 ]. % 8.76/8.91 apply (zenon_L752_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Had | zenon_intro zenon_Hd1 ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.76/8.91 apply (zenon_L80_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.76/8.91 apply (zenon_L752_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.76/8.91 apply (zenon_L748_); trivial. % 8.76/8.91 apply (zenon_L685_); trivial. % 8.76/8.91 apply (zenon_L263_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.76/8.91 apply (zenon_L70_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.76/8.91 apply (zenon_L21_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.76/8.91 apply (zenon_L760_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.76/8.91 apply (zenon_L484_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H35d); [ zenon_intro zenon_Hac | zenon_intro zenon_H35f ]. % 8.76/8.91 apply (zenon_L764_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_H358 | zenon_intro zenon_H360 ]. % 8.76/8.91 apply (zenon_L762_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Had | zenon_intro zenon_Hd1 ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.76/8.91 apply (zenon_L76_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.76/8.91 apply (zenon_L762_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.91 apply (zenon_L738_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.91 apply (zenon_L5_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.76/8.91 apply (zenon_L759_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.76/8.91 apply (zenon_L724_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.76/8.91 apply (zenon_L28_); trivial. % 8.76/8.91 apply (zenon_L88_); trivial. % 8.76/8.91 apply (zenon_L553_); trivial. % 8.76/8.91 apply (zenon_L685_); trivial. % 8.76/8.91 apply (zenon_L263_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.76/8.91 apply (zenon_L527_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.76/8.91 apply (zenon_L19_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.76/8.91 apply (zenon_L639_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.76/8.91 apply (zenon_L765_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.76/8.91 apply (zenon_L21_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.76/8.91 apply (zenon_L21_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.76/8.91 apply (zenon_L770_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.76/8.91 apply (zenon_L495_); trivial. % 8.76/8.91 apply (zenon_L55_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.76/8.91 apply (zenon_L23_); trivial. % 8.76/8.91 apply (zenon_L771_); trivial. % 8.76/8.91 apply (zenon_L246_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.76/8.91 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 8.76/8.91 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H41. zenon_intro zenon_H4a. % 8.76/8.91 apply (zenon_and_s _ _ zenon_H4a). zenon_intro zenon_H154. zenon_intro zenon_H2c3. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H175 | zenon_intro zenon_H230 ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.76/8.91 apply (zenon_L21_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.91 apply (zenon_L656_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.91 apply (zenon_L9_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H143 | zenon_intro zenon_H286 ]. % 8.76/8.91 apply (zenon_L673_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H165 | zenon_intro zenon_H287 ]. % 8.76/8.91 apply (zenon_L775_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H80 | zenon_intro zenon_H10f ]. % 8.76/8.91 apply (zenon_L40_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.76/8.91 apply (zenon_L715_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.76/8.91 apply (zenon_L258_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.76/8.91 apply (zenon_L346_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hfe | zenon_intro zenon_H32a ]. % 8.76/8.91 apply (zenon_L776_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H108 | zenon_intro zenon_H32b ]. % 8.76/8.91 apply (zenon_L584_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H3c | zenon_intro zenon_He8 ]. % 8.76/8.91 apply (zenon_L368_); trivial. % 8.76/8.91 apply (zenon_L687_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.76/8.91 apply (zenon_L45_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.76/8.91 apply (zenon_L28_); trivial. % 8.76/8.91 apply (zenon_L584_); trivial. % 8.76/8.91 apply (zenon_L553_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.76/8.91 apply (zenon_L565_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.76/8.91 apply (zenon_L21_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.76/8.91 apply (zenon_L1_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.76/8.91 apply (zenon_L785_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.91 apply (zenon_L738_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.91 apply (zenon_L9_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.91 apply (zenon_L786_); trivial. % 8.76/8.91 apply (zenon_L553_); trivial. % 8.76/8.91 apply (zenon_L685_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.76/8.91 apply (zenon_L495_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.76/8.91 apply (zenon_L113_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.91 apply (zenon_L780_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.91 apply (zenon_L10_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.91 apply (zenon_L789_); trivial. % 8.76/8.91 apply (zenon_L553_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.91 apply (zenon_L738_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.91 apply (zenon_L9_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.91 apply (zenon_L791_); trivial. % 8.76/8.91 apply (zenon_L553_); trivial. % 8.76/8.91 apply (zenon_L685_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.76/8.91 apply (zenon_L780_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.76/8.91 apply (zenon_L19_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.76/8.91 apply (zenon_L119_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.91 apply (zenon_L778_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.91 apply (zenon_L10_); trivial. % 8.76/8.91 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.92 apply (zenon_L157_); trivial. % 8.76/8.92 apply (zenon_L553_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.76/8.92 apply (zenon_L21_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.76/8.92 apply (zenon_L21_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.76/8.92 apply (zenon_L113_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.76/8.92 apply (zenon_L792_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.92 apply (zenon_L656_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.92 apply (zenon_L9_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.92 apply (zenon_L767_); trivial. % 8.76/8.92 apply (zenon_L553_); trivial. % 8.76/8.92 apply (zenon_L685_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.76/8.92 apply (zenon_L484_); trivial. % 8.76/8.92 apply (zenon_L55_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.76/8.92 apply (zenon_L23_); trivial. % 8.76/8.92 apply (zenon_L771_); trivial. % 8.76/8.92 apply (zenon_L246_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H178 | zenon_intro zenon_H231 ]. % 8.76/8.92 apply (zenon_L793_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17b | zenon_intro zenon_H232 ]. % 8.76/8.92 apply (zenon_L116_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17e | zenon_intro zenon_H233 ]. % 8.76/8.92 apply (zenon_L118_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H181 | zenon_intro zenon_H234 ]. % 8.76/8.92 apply (zenon_L120_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H184 | zenon_intro zenon_H235 ]. % 8.76/8.92 apply (zenon_L121_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H187 | zenon_intro zenon_H236 ]. % 8.76/8.92 apply (zenon_L277_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H237 ]. % 8.76/8.92 apply (zenon_L389_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H19d | zenon_intro zenon_H238 ]. % 8.76/8.92 apply (zenon_L129_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H239 ]. % 8.76/8.92 apply (zenon_L278_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H23a ]. % 8.76/8.92 apply (zenon_L794_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H23b ]. % 8.76/8.92 apply (zenon_L795_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1ab | zenon_intro zenon_H23c ]. % 8.76/8.92 apply (zenon_L135_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1ae | zenon_intro zenon_H23d ]. % 8.76/8.92 apply (zenon_L546_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H23e ]. % 8.76/8.92 apply (zenon_L443_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H23f ]. % 8.76/8.92 apply (zenon_L444_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H240 ]. % 8.76/8.92 apply (zenon_L796_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H241 ]. % 8.76/8.92 apply (zenon_L520_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H241); [ zenon_intro zenon_H1bb | zenon_intro zenon_H242 ]. % 8.76/8.92 apply (zenon_L141_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H242); [ zenon_intro zenon_H1bd | zenon_intro zenon_H243 ]. % 8.76/8.92 apply (zenon_L797_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H1bf | zenon_intro zenon_H244 ]. % 8.76/8.92 apply (zenon_L143_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H245 ]. % 8.76/8.92 apply (zenon_L144_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H246 ]. % 8.76/8.92 apply (zenon_L146_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H247 ]. % 8.76/8.92 apply (zenon_L147_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H248 ]. % 8.76/8.92 apply (zenon_L390_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H1ca | zenon_intro zenon_H249 ]. % 8.76/8.92 apply (zenon_L151_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1cc | zenon_intro zenon_H24a ]. % 8.76/8.92 apply (zenon_L798_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1ce | zenon_intro zenon_H24b ]. % 8.76/8.92 apply (zenon_L799_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ]. % 8.76/8.92 apply (zenon_L355_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H24d ]. % 8.76/8.92 apply (zenon_L356_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H24e ]. % 8.76/8.92 apply (zenon_L446_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H24f ]. % 8.76/8.92 apply (zenon_L447_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H1ea | zenon_intro zenon_H250 ]. % 8.76/8.92 apply (zenon_L800_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1ec | zenon_intro zenon_H251 ]. % 8.76/8.92 apply (zenon_L801_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H1ee | zenon_intro zenon_H252 ]. % 8.76/8.92 apply (zenon_L188_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H253 ]. % 8.76/8.92 apply (zenon_L598_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H254 ]. % 8.76/8.92 apply (zenon_L547_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H255 ]. % 8.76/8.92 apply (zenon_L317_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H256 ]. % 8.76/8.92 apply (zenon_L364_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H1fb | zenon_intro zenon_H257 ]. % 8.76/8.92 apply (zenon_L279_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1fd | zenon_intro zenon_H258 ]. % 8.76/8.92 apply (zenon_L241_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H1ff | zenon_intro zenon_H259 ]. % 8.76/8.92 apply (zenon_L242_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H201 | zenon_intro zenon_H25a ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.76/8.92 apply (zenon_L21_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.92 apply (zenon_L803_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.92 apply (zenon_L10_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H143 | zenon_intro zenon_H286 ]. % 8.76/8.92 apply (zenon_L673_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H165 | zenon_intro zenon_H287 ]. % 8.76/8.92 apply (zenon_L805_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H80 | zenon_intro zenon_H10f ]. % 8.76/8.92 apply (zenon_L40_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H27e | zenon_intro zenon_H36b ]. % 8.76/8.92 apply (zenon_L715_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H36b); [ zenon_intro zenon_H196 | zenon_intro zenon_H36c ]. % 8.76/8.92 apply (zenon_L258_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H36c); [ zenon_intro zenon_H99 | zenon_intro zenon_H195 ]. % 8.76/8.92 apply (zenon_L346_); trivial. % 8.76/8.92 apply (zenon_L804_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.76/8.92 apply (zenon_L724_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.76/8.92 apply (zenon_L97_); trivial. % 8.76/8.92 apply (zenon_L584_); trivial. % 8.76/8.92 apply (zenon_L553_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.76/8.92 apply (zenon_L565_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.76/8.92 apply (zenon_L21_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.76/8.92 apply (zenon_L1_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.76/8.92 apply (zenon_L806_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.92 apply (zenon_L803_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.92 apply (zenon_L10_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.92 apply (zenon_L786_); trivial. % 8.76/8.92 apply (zenon_L553_); trivial. % 8.76/8.92 apply (zenon_L685_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.76/8.92 apply (zenon_L366_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.76/8.92 apply (zenon_L1_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.92 apply (zenon_L803_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.92 apply (zenon_L10_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.92 apply (zenon_L789_); trivial. % 8.76/8.92 apply (zenon_L553_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.92 apply (zenon_L802_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.92 apply (zenon_L9_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.92 apply (zenon_L791_); trivial. % 8.76/8.92 apply (zenon_L553_); trivial. % 8.76/8.92 apply (zenon_L685_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.76/8.92 apply (zenon_L803_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.76/8.92 apply (zenon_L19_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.76/8.92 apply (zenon_L119_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.76/8.92 apply (zenon_L21_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.76/8.92 apply (zenon_L777_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.76/8.92 apply (zenon_L565_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.92 apply (zenon_L816_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.92 apply (zenon_L10_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.92 apply (zenon_L157_); trivial. % 8.76/8.92 apply (zenon_L553_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.76/8.92 apply (zenon_L21_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H77 | zenon_intro zenon_Hfa ]. % 8.76/8.92 apply (zenon_L21_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hfb ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H35d); [ zenon_intro zenon_Hac | zenon_intro zenon_H35f ]. % 8.76/8.92 apply (zenon_L305_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_H358 | zenon_intro zenon_H360 ]. % 8.76/8.92 apply (zenon_L792_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Had | zenon_intro zenon_Hd1 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.76/8.92 apply (zenon_L80_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.92 apply (zenon_L656_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.92 apply (zenon_L9_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H143 | zenon_intro zenon_H286 ]. % 8.76/8.92 apply (zenon_L673_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H165 | zenon_intro zenon_H287 ]. % 8.76/8.92 apply (zenon_L817_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H80 | zenon_intro zenon_H10f ]. % 8.76/8.92 apply (zenon_L40_); trivial. % 8.76/8.92 apply (zenon_L768_); trivial. % 8.76/8.92 apply (zenon_L553_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.92 apply (zenon_L779_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.92 apply (zenon_L10_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.92 apply (zenon_L817_); trivial. % 8.76/8.92 apply (zenon_L553_); trivial. % 8.76/8.92 apply (zenon_L685_); trivial. % 8.76/8.92 apply (zenon_L263_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hf1 ]. % 8.76/8.92 apply (zenon_L366_); trivial. % 8.76/8.92 apply (zenon_L55_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.76/8.92 apply (zenon_L23_); trivial. % 8.76/8.92 apply (zenon_L771_); trivial. % 8.76/8.92 apply (zenon_L246_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H203 | zenon_intro zenon_H25b ]. % 8.76/8.92 apply (zenon_L271_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H205 | zenon_intro zenon_H25c ]. % 8.76/8.92 apply (zenon_L818_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 8.76/8.92 apply (zenon_L548_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H209 | zenon_intro zenon_H25e ]. % 8.76/8.92 apply (zenon_L369_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H20b | zenon_intro zenon_H25f ]. % 8.76/8.92 apply (zenon_L452_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H20d | zenon_intro zenon_H260 ]. % 8.76/8.92 apply (zenon_L819_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 8.76/8.92 apply (zenon_L281_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H211 | zenon_intro zenon_H262 ]. % 8.76/8.92 apply (zenon_L537_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H213 | zenon_intro zenon_H263 ]. % 8.76/8.92 apply (zenon_L373_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H215 | zenon_intro zenon_H264 ]. % 8.76/8.92 apply (zenon_L549_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H217 | zenon_intro zenon_H265 ]. % 8.76/8.92 apply (zenon_L408_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_H219 | zenon_intro zenon_H266 ]. % 8.76/8.92 apply (zenon_L377_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H21b | zenon_intro zenon_H267 ]. % 8.76/8.92 apply (zenon_L378_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H21d | zenon_intro zenon_H268 ]. % 8.76/8.92 apply (zenon_L453_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H21f | zenon_intro zenon_H269 ]. % 8.76/8.92 apply (zenon_L597_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H221 | zenon_intro zenon_H26a ]. % 8.76/8.92 apply (zenon_L542_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H223 | zenon_intro zenon_H26b ]. % 8.76/8.92 apply (zenon_L382_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H225 | zenon_intro zenon_H26c ]. % 8.76/8.92 apply (zenon_L383_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H227 | zenon_intro zenon_H26d ]. % 8.76/8.92 apply (zenon_L386_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_H229 | zenon_intro zenon_H22b ]. % 8.76/8.92 apply (zenon_L454_); trivial. % 8.76/8.92 apply (zenon_L455_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.76/8.92 apply (zenon_L13_); trivial. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H59. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.76/8.92 apply (zenon_L21_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H35d); [ zenon_intro zenon_Hac | zenon_intro zenon_H35f ]. % 8.76/8.92 apply (zenon_L749_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_H358 | zenon_intro zenon_H360 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.92 apply (zenon_L656_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.92 apply (zenon_L5_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H10d ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H143 | zenon_intro zenon_H286 ]. % 8.76/8.92 apply (zenon_L673_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H165 | zenon_intro zenon_H287 ]. % 8.76/8.92 apply (zenon_L828_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H80 | zenon_intro zenon_H10f ]. % 8.76/8.92 apply (zenon_L40_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_H24 | zenon_intro zenon_Hc6 ]. % 8.76/8.92 apply (zenon_L2_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Had | zenon_intro zenon_Hc7 ]. % 8.76/8.92 apply (zenon_L833_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H80 | zenon_intro zenon_Hc3 ]. % 8.76/8.92 apply (zenon_L40_); trivial. % 8.76/8.92 apply (zenon_L834_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_Hcc | zenon_intro zenon_H10e ]. % 8.76/8.92 apply (zenon_L45_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H93 | zenon_intro zenon_H108 ]. % 8.76/8.92 apply (zenon_L28_); trivial. % 8.76/8.92 apply (zenon_L584_); trivial. % 8.76/8.92 apply (zenon_L553_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_Had | zenon_intro zenon_Hd1 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.76/8.92 apply (zenon_L80_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.76/8.92 apply (zenon_L840_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H6b | zenon_intro zenon_H337 ]. % 8.76/8.92 apply (zenon_L838_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H337); [ zenon_intro zenon_H2a | zenon_intro zenon_H338 ]. % 8.76/8.92 apply (zenon_L5_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H338); [ zenon_intro zenon_H15a | zenon_intro zenon_Hf4 ]. % 8.76/8.92 apply (zenon_L839_); trivial. % 8.76/8.92 apply (zenon_L265_); trivial. % 8.76/8.92 apply (zenon_L685_); trivial. % 8.76/8.92 apply (zenon_L263_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.76/8.92 apply (zenon_L565_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.76/8.92 apply (zenon_L1_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.76/8.92 apply (zenon_L849_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.76/8.92 apply (zenon_L845_); trivial. % 8.76/8.92 apply (zenon_L685_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.76/8.92 apply (zenon_L838_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.76/8.92 apply (zenon_L825_); trivial. % 8.76/8.92 apply (zenon_L246_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.76/8.92 apply (zenon_L6_); trivial. % 8.76/8.92 apply (zenon_L384_); trivial. % 8.76/8.92 apply (zenon_L375_); trivial. % 8.76/8.92 (* end of lemma zenon_L850_ *) % 8.76/8.92 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H38e. zenon_intro zenon_H38d. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H38d). zenon_intro zenon_H2e2. zenon_intro zenon_H38f. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H38f). zenon_intro zenon_H300. zenon_intro zenon_H390. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H390). zenon_intro zenon_H105. zenon_intro zenon_H391. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H391). zenon_intro zenon_Hb7. zenon_intro zenon_H392. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H392). zenon_intro zenon_H389. zenon_intro zenon_H393. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H393). zenon_intro zenon_H2f8. zenon_intro zenon_H394. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H394). zenon_intro zenon_H2b5. zenon_intro zenon_H395. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H395). zenon_intro zenon_H282. zenon_intro zenon_H396. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H396). zenon_intro zenon_H19a. zenon_intro zenon_H397. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H397). zenon_intro zenon_H9f. zenon_intro zenon_H398. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H398). zenon_intro zenon_H2d8. zenon_intro zenon_H399. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H399). zenon_intro zenon_H39b. zenon_intro zenon_H39a. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H39a). zenon_intro zenon_H1dc. zenon_intro zenon_H39c. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H39c). zenon_intro zenon_H2d4. zenon_intro zenon_Hed. % 8.76/8.92 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H39e. zenon_intro zenon_H39d. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H39d). zenon_intro zenon_H2a2. zenon_intro zenon_H39f. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H39f). zenon_intro zenon_H2a1. zenon_intro zenon_H3a0. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3a0). zenon_intro zenon_H150. zenon_intro zenon_H3a1. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3a1). zenon_intro zenon_H11e. zenon_intro zenon_H3a2. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3a2). zenon_intro zenon_Hf8. zenon_intro zenon_H3a3. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3a3). zenon_intro zenon_H2a4. zenon_intro zenon_H3a4. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3a4). zenon_intro zenon_H32e. zenon_intro zenon_H3a5. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3a5). zenon_intro zenon_H35d. zenon_intro zenon_H3a6. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3a6). zenon_intro zenon_H35e. zenon_intro zenon_H3a7. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3a7). zenon_intro zenon_H3a9. zenon_intro zenon_H3a8. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3a8). zenon_intro zenon_H336. zenon_intro zenon_H3aa. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3aa). zenon_intro zenon_H10c. zenon_intro zenon_H3ab. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3ab). zenon_intro zenon_H2c0. zenon_intro zenon_H3ac. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3ac). zenon_intro zenon_Hba. zenon_intro zenon_H3ad. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3ad). zenon_intro zenon_H2a3. zenon_intro zenon_H3ae. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3ae). zenon_intro zenon_H285. zenon_intro zenon_H3af. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3af). zenon_intro zenon_Hc5. zenon_intro zenon_H3b0. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3b0). zenon_intro zenon_H303. zenon_intro zenon_H3b1. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3b1). zenon_intro zenon_H2df. zenon_intro zenon_H3b2. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3b2). zenon_intro zenon_H3b4. zenon_intro zenon_H3b3. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3b3). zenon_intro zenon_Hbf. zenon_intro zenon_H3b5. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3b5). zenon_intro zenon_H36a. zenon_intro zenon_H3b6. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3b6). zenon_intro zenon_H2e8. zenon_intro zenon_H3b7. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3b7). zenon_intro zenon_H371. zenon_intro zenon_H3b8. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3b8). zenon_intro zenon_H11f. zenon_intro zenon_H3b9. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3b9). zenon_intro zenon_Hf9. zenon_intro zenon_H3ba. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3ba). zenon_intro zenon_H2b8. zenon_intro zenon_H3bb. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3bb). zenon_intro zenon_H322. zenon_intro zenon_H3bc. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3bc). zenon_intro zenon_H329. zenon_intro zenon_H3bd. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3bd). zenon_intro zenon_H3be. zenon_intro zenon_H331. % 8.76/8.92 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H34d. zenon_intro zenon_H3bf. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3bf). zenon_intro zenon_H137. zenon_intro zenon_H3c0. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3c0). zenon_intro zenon_H270. zenon_intro zenon_H3c1. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3c1). zenon_intro zenon_H145. zenon_intro zenon_H3c2. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3c2). zenon_intro zenon_H295. zenon_intro zenon_H3c3. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3c3). zenon_intro zenon_H27f. zenon_intro zenon_H3c4. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3c4). zenon_intro zenon_H6c. zenon_intro zenon_H3c5. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3c5). zenon_intro zenon_H164. zenon_intro zenon_H3c6. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3c6). zenon_intro zenon_H1dd. zenon_intro zenon_H3c7. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3c7). zenon_intro zenon_H2c9. zenon_intro zenon_H3c8. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3c8). zenon_intro zenon_Hf3. zenon_intro zenon_H3c9. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3c9). zenon_intro zenon_H169. zenon_intro zenon_H3ca. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3ca). zenon_intro zenon_H134. zenon_intro zenon_H3cb. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3cb). zenon_intro zenon_H90. zenon_intro zenon_H3cc. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3cc). zenon_intro zenon_H29f. zenon_intro zenon_H3cd. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3cd). zenon_intro zenon_H94. zenon_intro zenon_H3ce. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3ce). zenon_intro zenon_H2d2. zenon_intro zenon_H3cf. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3cf). zenon_intro zenon_H9a. zenon_intro zenon_H3d0. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3d0). zenon_intro zenon_Hd0. zenon_intro zenon_H3d1. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3d1). zenon_intro zenon_Hff. zenon_intro zenon_H3d2. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3d2). zenon_intro zenon_He4. zenon_intro zenon_H3d3. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3d3). zenon_intro zenon_H109. zenon_intro zenon_H3d4. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3d4). zenon_intro zenon_H16d. zenon_intro zenon_H3d5. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3d5). zenon_intro zenon_He7. zenon_intro zenon_H3d6. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3d6). zenon_intro zenon_H1f. zenon_intro zenon_H3d7. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3d7). zenon_intro zenon_H25. zenon_intro zenon_H3d8. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3d8). zenon_intro zenon_H31. zenon_intro zenon_H3d9. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3d9). zenon_intro zenon_H124. zenon_intro zenon_H3da. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3da). zenon_intro zenon_H127. zenon_intro zenon_H3db. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3db). zenon_intro zenon_H153. zenon_intro zenon_H3dc. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3dc). zenon_intro zenon_H74. zenon_intro zenon_H3dd. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3dd). zenon_intro zenon_Hab. zenon_intro zenon_H3de. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3de). zenon_intro zenon_Hb4. zenon_intro zenon_H3df. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3df). zenon_intro zenon_H2b. zenon_intro zenon_H3e0. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3e0). zenon_intro zenon_H36. zenon_intro zenon_H3e1. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3e1). zenon_intro zenon_H129. zenon_intro zenon_H3e2. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3e2). zenon_intro zenon_H192. zenon_intro zenon_H3e3. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3e3). zenon_intro zenon_H173. zenon_intro zenon_H3e4. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3e4). zenon_intro zenon_H12b. zenon_intro zenon_H3e5. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3e5). zenon_intro zenon_H1f6. zenon_intro zenon_H3e6. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3e6). zenon_intro zenon_H197. zenon_intro zenon_H3e7. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3e7). zenon_intro zenon_H3a. zenon_intro zenon_H3e8. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3e8). zenon_intro zenon_H1d3. zenon_intro zenon_H3e9. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3e9). zenon_intro zenon_H170. zenon_intro zenon_H3ea. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3ea). zenon_intro zenon_H1d7. zenon_intro zenon_H3eb. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3eb). zenon_intro zenon_H1d9. zenon_intro zenon_H3ec. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3ec). zenon_intro zenon_H2fc. zenon_intro zenon_Heb. % 8.76/8.92 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H67. zenon_intro zenon_H3ed. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3ed). zenon_intro zenon_H78. zenon_intro zenon_H3ee. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3ee). zenon_intro zenon_Hc2. zenon_intro zenon_H3ef. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3ef). zenon_intro zenon_H7d. zenon_intro zenon_H3f0. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3f0). zenon_intro zenon_Ha3. zenon_intro zenon_Ha8. % 8.76/8.92 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H3f2. zenon_intro zenon_H3f1. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3f1). zenon_intro zenon_H2f3. zenon_intro zenon_H3f3. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3f3). zenon_intro zenon_H2bf. zenon_intro zenon_H3f4. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3f4). zenon_intro zenon_H22d. zenon_intro zenon_H3f5. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H3f5). zenon_intro zenon_H2a5. zenon_intro zenon_H22e. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H3f2); [ zenon_intro zenon_H1e | zenon_intro zenon_H3f6 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H1d | zenon_intro zenon_H2f4 ]. % 8.76/8.92 apply (zenon_L1_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2f4); [ zenon_intro zenon_H2a | zenon_intro zenon_H2f5 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c1 ]. % 8.76/8.92 apply (zenon_L2_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H29 | zenon_intro zenon_H2c2 ]. % 8.76/8.92 apply (zenon_L3_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2c2); [ zenon_intro zenon_H3b | zenon_intro zenon_H98 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.76/8.92 apply (zenon_L4_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.76/8.92 apply (zenon_L5_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.76/8.92 apply (zenon_L6_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.76/8.92 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (op (e0) (e0))) = (e0))). % 8.76/8.92 intro zenon_D_pnotp. % 8.76/8.92 apply zenon_H12e. % 8.76/8.92 rewrite <- zenon_D_pnotp. % 8.76/8.92 exact zenon_H1e. % 8.76/8.92 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.76/8.92 cut (((op (e0) (e0)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H3f7]. % 8.76/8.92 congruence. % 8.76/8.92 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H130 | zenon_intro zenon_H131 ]. % 8.76/8.92 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e0)) = (op (e0) (op (e0) (e0))))). % 8.76/8.92 intro zenon_D_pnotp. % 8.76/8.92 apply zenon_H3f7. % 8.76/8.92 rewrite <- zenon_D_pnotp. % 8.76/8.92 exact zenon_H130. % 8.76/8.92 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 8.76/8.92 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H3f8]. % 8.76/8.92 congruence. % 8.76/8.92 cut (((op (e0) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f9]. % 8.76/8.92 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 8.76/8.92 congruence. % 8.76/8.92 apply zenon_H3f. apply refl_equal. % 8.76/8.92 exact (zenon_H3f9 zenon_H1e). % 8.76/8.92 apply zenon_H131. apply refl_equal. % 8.76/8.92 apply zenon_H131. apply refl_equal. % 8.76/8.92 apply zenon_H3f. apply refl_equal. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.76/8.92 apply (zenon_L10_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.76/8.92 apply (zenon_L13_); trivial. % 8.76/8.92 apply (zenon_L16_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.76/8.92 apply (zenon_L4_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.76/8.92 apply (zenon_L5_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2a7 | zenon_intro zenon_H2a6 ]. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H12e. zenon_intro zenon_H2a8. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H118. zenon_intro zenon_H18a. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.76/8.92 apply (zenon_L17_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.76/8.92 apply (zenon_L18_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.76/8.92 apply (zenon_L19_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.76/8.92 apply (zenon_L20_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.76/8.92 apply (zenon_L71_); trivial. % 8.76/8.92 apply (zenon_L496_); trivial. % 8.76/8.92 apply (zenon_L498_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H47 | zenon_intro zenon_H2af ]. % 8.76/8.92 apply (zenon_L10_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H4c. zenon_intro zenon_H57. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.76/8.92 apply (zenon_L17_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.76/8.92 apply (zenon_L18_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.76/8.92 apply (zenon_L643_); trivial. % 8.76/8.92 apply (zenon_L498_); trivial. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 8.76/8.92 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H59. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.76/8.92 apply (zenon_L17_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.76/8.92 apply (zenon_L18_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.76/8.92 apply (zenon_L19_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.76/8.92 apply (zenon_L639_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.76/8.92 apply (zenon_L651_); trivial. % 8.76/8.92 apply (zenon_L652_); trivial. % 8.76/8.92 apply (zenon_L655_); trivial. % 8.76/8.92 apply (zenon_L53_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H191 | zenon_intro zenon_H1b1 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c1 ]. % 8.76/8.92 apply (zenon_L2_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H29 | zenon_intro zenon_H2c2 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H30 | zenon_intro zenon_H22f ]. % 8.76/8.92 apply (zenon_L4_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H35 | zenon_intro zenon_H26e ]. % 8.76/8.92 apply (zenon_L74_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 8.76/8.92 apply (zenon_L191_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H66 | zenon_intro zenon_H2ab ]. % 8.76/8.92 apply (zenon_L17_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6b | zenon_intro zenon_H2ac ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.76/8.92 apply (zenon_L17_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.76/8.92 apply (zenon_L638_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.76/8.92 apply (zenon_L21_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.76/8.92 apply (zenon_L656_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.76/8.92 apply (zenon_L670_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H143 | zenon_intro zenon_H286 ]. % 8.76/8.92 apply (zenon_L261_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H165 | zenon_intro zenon_H287 ]. % 8.76/8.92 apply (zenon_L626_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H80 | zenon_intro zenon_H10f ]. % 8.76/8.92 apply (zenon_L668_); trivial. % 8.76/8.92 apply (zenon_L672_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.76/8.92 apply (zenon_L21_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.76/8.92 apply (zenon_L314_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.76/8.92 apply (zenon_L657_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H143 | zenon_intro zenon_H286 ]. % 8.76/8.92 apply (zenon_L673_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H165 | zenon_intro zenon_H287 ]. % 8.76/8.92 apply (zenon_L626_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H80 | zenon_intro zenon_H10f ]. % 8.76/8.92 apply (zenon_L667_); trivial. % 8.76/8.92 apply (zenon_L672_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H71 | zenon_intro zenon_Hd6 ]. % 8.76/8.92 apply (zenon_L78_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H66 | zenon_intro zenon_H151 ]. % 8.76/8.92 apply (zenon_L87_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H73 | zenon_intro zenon_H152 ]. % 8.76/8.92 apply (zenon_L93_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hf0 ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H77 | zenon_intro zenon_H120 ]. % 8.76/8.92 apply (zenon_L21_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcb | zenon_intro zenon_H121 ]. % 8.76/8.92 apply (zenon_L314_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H7e | zenon_intro zenon_Hfe ]. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H1d | zenon_intro zenon_H361 ]. % 8.76/8.92 apply (zenon_L1_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H361); [ zenon_intro zenon_H358 | zenon_intro zenon_H362 ]. % 8.76/8.92 apply (zenon_L664_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H362); [ zenon_intro zenon_H165 | zenon_intro zenon_H1df ]. % 8.76/8.92 apply (zenon_L626_); trivial. % 8.76/8.92 apply (zenon_L676_); trivial. % 8.76/8.92 apply (zenon_L81_); trivial. % 8.76/8.92 apply (zenon_L677_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H2c2); [ zenon_intro zenon_H3b | zenon_intro zenon_H98 ]. % 8.76/8.92 apply (zenon_L198_); trivial. % 8.76/8.92 apply (zenon_L711_); trivial. % 8.76/8.92 apply (zenon_L850_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H3f6); [ zenon_intro zenon_H73 | zenon_intro zenon_H3fa ]. % 8.76/8.92 apply (zenon_L639_); trivial. % 8.76/8.92 apply (zenon_or_s _ _ zenon_H3fa); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H1a9 ]. % 8.76/8.92 apply (zenon_L495_); trivial. % 8.76/8.92 apply (zenon_L354_); trivial. % 8.76/8.92 Qed. % 8.76/8.92 % SZS output end Proof % 8.76/8.92 (* END-PROOF *) % 8.76/8.92 nodes searched: 226720 % 8.76/8.92 max branch formulas: 331 % 8.76/8.92 proof nodes created: 9016 % 8.76/8.92 formulas created: 98407 % 8.76/8.92 %------------------------------------------------------------------------------